@article {2024, title = {Optimisation{\textendash}Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics}, year = {2024}, author = {Ivan Prusak and Davide Torlo and Monica Nonino and Gianluigi Rozza} } @unpublished {2023, title = {Applicable Methodologies for the Mass Transfer Phenomenon in Tumble Dryers: A Review}, year = {2023}, abstract = {

Tumble dryers offer a fast and convenient way of drying textiles independent of weather conditions and therefore are frequently used in ordinary households. However, artificial drying of textiles consumes considerable amounts of energy, approximately 8.2 percent of the residential electricity consumption is for drying of textiles in northern European countries (Cranston et al., 2019). Several authors have investigated the aspects of the clothes drying cycle with experimental and numerical methods to understand and improve the process. The first turning point study on understanding the physics of evaporation for tumble dryers was presented by Lambert et al. (1991) in the early 90s. With the aid of Chilton_Colburn analogy, they introduced the concept of area-mass transfer coefficient to address evaporation rate. Afterwards, several experimental or numerical studies were published based on this concept, and furthermore, the model was then developed into 0-dimensional (Deans, 2001) and 1-dimensional (Wei et al., 2017) to gain more accuracy. The evaporation rate is considered to be the main system parameter for dryers with which other performance parameters including drying time, effectiveness, moisture content and efficiency can be estimated. More recent literature focused on utilizing dimensional analysis or image processing techniques to correlate drying indices with system parameters. However, the validity of these regressed models is machine-specific, and hence, cannot be generalized yet. All the previous models for estimating the evaporation rate in tumble dryers are discussed. The review of the related literature showed that all of the previous models for the prediction of the evaporation rate in the clothes dryers have some limitations in terms of accuracy and applicability.

}, author = {Sajad Salavatidezfouli and Sajad Hajisharifi and Michele Girfoglio and Giovanni Stabile and Gianluigi Rozza} } @booklet {2023, title = {An optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems}, year = {2023}, author = {Ivan Prusak and Davide Torlo and Monica Nonino and Gianluigi Rozza} } @article {2023, title = {An optimisation{\textendash}based domain{\textendash}decomposition reduced order model for the incompressible Navier-Stokes equations}, volume = {151}, year = {2023}, month = {2023/12/01/}, pages = {172 - 189}, abstract = {

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain{\textendash}decomposition (DD) methods and reduced{\textendash}order modelling (ROM). In particular, we consider an optimisation{\textendash}based domain{\textendash}decomposition algorithm for the parameter{\textendash}dependent stationary incompressible Navier{\textendash}Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal{\textendash}control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward{\textendash}facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain{\textendash}decomposition algorithm.

}, keywords = {Computational fluid dynamics, Domain decomposition, Optimal control, Proper orthogonal decomposition, Reduced order modelling}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122123004248}, author = {Ivan Prusak and Monica Nonino and Davide Torlo and Francesco Ballarin and Gianluigi Rozza} } @article {2022, title = {A comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions}, journal = {ETNA - Electronic Transactions on Numerical Analysis}, volume = {56}, year = {2022}, pages = {52{\textendash}65}, doi = {10.1553/etna_vol56s52}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @booklet {2022, title = {Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics}, year = {2022}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @booklet {2022, title = {A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation}, year = {2022}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @article {2022, title = {Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier{\textendash}Stokes equations with model order reduction}, journal = {ESAIM: M2AN}, volume = {56}, year = {2022}, month = {2022///}, pages = {1361 - 1400}, url = {https://doi.org/10.1051/m2an/2022044}, author = {Federico Pichi and Maria Strazzullo and F. Ballarin and Gianluigi Rozza} } @article {2022, title = {Kernel-based active subspaces with application to computational fluid dynamics parametric problems using discontinuous Galerkin method}, journal = {International Journal for Numerical Methods in Engineering}, volume = {123}, year = {2022}, pages = {6000-6027}, doi = {10.1002/nme.7099}, author = {Francesco Romor and Marco Tezzele and Andrea Lario and Gianluigi Rozza} } @article {2022, title = {Mathematical modelling of oscillating patterns for chronic autoimmune diseases}, journal = {Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci}, volume = {n/a}, year = {2022}, month = {2022/04/01}, abstract = {

Many autoimmune diseases are chronic in nature, so that in general, patients experience periods of recurrence and remission of the symptoms characterizing their specific autoimmune ailment. In order to describe this very important feature of autoimmunity, we construct a mathematical model of kinetic type describing the immune system cellular interactions in the context of autoimmunity exhibiting recurrent dynamics. The model equations constitute a nonlinear system of integro-differential equations with quadratic terms that describe the interactions between self-antigen presenting cells, self-reactive T cells, and immunosuppressive cells. We consider a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with predisposition for this condition. We also consider the natural death of all cell populations involved in our model, caused by their interaction with cells of the host environment. We derive the macroscopic analogue and show positivity and well-posedness of the solution and then we study the equilibria of the corresponding dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the occurrence of a Hopf bifurcation. We perform some numerical simulations for our model, and we observe a recurrent pattern in the solutions of both the kinetic description and its macroscopic analogue, which leads us to conclude that this model is able to capture the chronic behaviour of many autoimmune diseases.

}, keywords = {autoimmune diseases, cellular interactions, Dynamical systems, Hopf bifurcation, kinetic theory, mathematical biology}, isbn = {0170-4214}, url = {https://doi.org/10.1002/mma.8229}, author = {Rossella Della Marca and Maria da Piedade Machado Ramos and Carolina Ribeiro and Ana Jacinta Soares} } @article {2022, title = {Model order reduction for bifurcating phenomena in fluid-structure interaction problems}, journal = {International Journal for Numerical Methods in FluidsInternational Journal for Numerical Methods in FluidsInt J Numer Meth Fluids}, volume = {n/a}, year = {2022}, month = {2022/05/23}, abstract = {

Abstract This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coand? effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t.\ the standard model, while the same effect is even magnified when considering linear elastic solid.

}, keywords = {Bifurcation theory, Coand{\u a} effect, continuum mechanics, fluid dynamics, monolithic method, parametrized fluid-structure interaction problem, Proper orthogonal decomposition, reduced order modeling}, isbn = {0271-2091}, url = {https://doi.org/10.1002/fld.5118}, author = {Moaad Khamlich and Federico Pichi and Gianluigi Rozza} } @unpublished {2022, title = {Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations}, year = {2022}, author = {Martin W. Hess and Gianluigi Rozza} } @article {2022, title = {The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {392}, year = {2022}, abstract = {

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N-width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation. {\textcopyright} 2022 Elsevier B.V.

}, keywords = {Advection, Computational complexity, Deep neural network, Deep neural networks, Linear subspace, Multiphase simulations, Non linear, Nonlinear hyperbolic equation, Partial differential equations, Phase space methods, Pre-processing, Principal component analysis, reduced order modeling, Reduced order modelling, Reduced-order model, Shifted-POD}, doi = {10.1016/j.cma.2022.114687}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633\&doi=10.1016\%2fj.cma.2022.114687\&partnerID=40\&md5=12f82dcaba04c4a7c44f8e5b20101997}, author = {Davide Papapicco and Nicola Demo and Michele Girfoglio and Giovanni Stabile and Gianluigi Rozza} } @article {2022, title = {A POD-Galerkin reduced order model for the Navier{\textendash}Stokes equations in stream function-vorticity formulation}, year = {2022}, month = {2022/06/14/}, pages = {105536}, abstract = {

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier{\textendash}Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization.

}, keywords = {Galerkin projection, Navier{\textendash}Stokes equations, Proper orthogonal decomposition, Reduced order model, Stream function-vorticity formulation}, isbn = {0045-7930}, url = {https://www.sciencedirect.com/science/article/pii/S0045793022001645}, author = {Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza} } @booklet {2022, title = {Projection based semi{\textendash}implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid{\textendash}Structure Interaction problems}, year = {2022}, abstract = {

The goal of this manuscript is to present a partitioned Model Order Reduction method that is based on a semi-implicit projection scheme to solve multiphysics problems. We implement a Reduced Order Method based on a Proper Orthogonal Decomposition, with the aim of addressing both time-dependent and time-dependent, parametrized Fluid-Structure Interaction problems, where the fluid is incompressible and the structure is thick and two dimensional.

}, author = {Monica Nonino and Francesco Ballarin and Gianluigi Rozza and Yvon Maday} } @conference {2022, title = {A Proper Orthogonal Decomposition Approach for Parameters Reduction of Single Shot Detector Networks}, booktitle = {2022 IEEE International Conference on Image Processing (ICIP)}, year = {2022}, doi = {10.1109/ICIP46576.2022.9897513}, author = {Laura Meneghetti and Nicola Demo and Gianluigi Rozza} } @unpublished {2021, title = {An artificial neural network approach to bifurcating phenomena in computational fluid dynamics}, year = {2021}, author = {Federico Pichi and Francesco Ballarin and Gianluigi Rozza and Jan S Hesthaven} } @article {romor2020athena, title = {ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis}, journal = {Software Impacts}, volume = {10}, year = {2021}, pages = {100133}, doi = {10.1016/j.simpa.2021.100133}, author = {Francesco Romor and Marco Tezzele and Gianluigi Rozza} } @unpublished {2021, title = {A CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION}, year = {2021}, author = {Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza} } @article {2021, title = {On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis}, journal = {Computers \& Fluids}, volume = {216}, year = {2021}, pages = {104819}, abstract = {

In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

}, keywords = {Dynamic mode decomposition, Ffowcs Williams and Hawkings, Hydroacoustics, Large eddy simulation, Model reduction, Proper orthogonal decomposition}, issn = {0045-7930}, doi = {https://doi.org/10.1016/j.compfluid.2020.104819}, url = {https://www.sciencedirect.com/science/article/pii/S0045793020303893}, author = {Mahmoud Gadalla and Marta Cianferra and Marco Tezzele and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @unpublished {2021, title = {Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows}, year = {2021}, author = {Maria Strazzullo and Michele Girfoglio and Francesco Ballarin and T. Iliescu and Gianluigi Rozza} } @unpublished {2021, title = {A data-driven partitioned approach for the resolution of time-dependent optimal control problems with dynamic mode decomposition}, year = {2021}, author = {Eleonora Donadini and Maria Strazzullo and Marco Tezzele and Gianluigi Rozza} } @booklet {2021, title = {A Dimensionality Reduction Approach for Convolutional Neural Networks}, year = {2021}, author = {Laura Meneghetti and Nicola Demo and Gianluigi Rozza} } @conference {2021, title = {Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, year = {2021}, month = {2021//}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time.

}, isbn = {978-3-030-55874-1}, author = {Nirav Shah and Martin W. Hess and Gianluigi Rozza}, editor = {Vermolen, Fred J. and Vuik, Cornelis} } @article {2021, title = {A dynamic mode decomposition extension for the forecasting of parametric dynamical systems}, journal = {arXiv preprint arXiv:2110.09155}, year = {2021}, author = {Francesco Andreuzzi and Nicola Demo and Gianluigi Rozza} } @article {2021, title = {Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method}, journal = {Advances in Computational Mathematics}, volume = {47}, year = {2021}, abstract = {

The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.\ 

}, doi = {10.1007/s10444-020-09827-6}, author = {Moreno Pintore and Federico Pichi and Martin W. Hess and Gianluigi Rozza and Claudio Canuto} } @article {2021, title = {An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques}, journal = {Bolletino dell Unione Matematica Italiana}, volume = {14}, year = {2021}, pages = {211-230}, abstract = {

This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive{\textemdash}especially dealing with complex industrial geometries{\textemdash}we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

}, doi = {10.1007/s40574-020-00263-4}, author = {Nicola Demo and Giulio Ortali and Gianluca Gustin and Gianluigi Rozza and Gianpiero Lavini} } @unpublished {2021, title = {AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS}, year = {2021}, author = {Nicola Demo and Maria Strazzullo and Gianluigi Rozza} } @article {2021, title = {Hierarchical model reduction techniques for flow modeling in a parametrized setting}, journal = {Multiscale Modeling and Simulation}, volume = {19}, year = {2021}, pages = {267-293}, abstract = {

In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.

}, doi = {10.1137/19M1285330}, author = {Matteo Zancanaro and F. Ballarin and Simona Perotto and Gianluigi Rozza} } @article {2021, title = {Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing}, journal = {Journal of Marine Science and Engineering}, volume = {9}, year = {2021}, pages = {185}, abstract = {

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

}, issn = {2077-1312}, doi = {10.3390/jmse9020185}, url = {https://www.mdpi.com/2077-1312/9/2/185}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {ZancanaroMrosekStabileOthmerRozza2021, title = {Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters}, journal = {Fluids}, volume = {6}, number = {8}, year = {2021}, pages = {296}, publisher = {MDPI AG}, doi = {10.3390/fluids6080296}, url = {https://doi.org/10.3390/fluids6080296}, author = {Matteo Zancanaro and Markus Mrosek and Giovanni Stabile and Carsten Othmer and Gianluigi Rozza} } @unpublished {romor2021las, title = {A local approach to parameter space reduction for regression and classification tasks}, year = {2021}, note = {Submitted}, author = {Francesco Romor and Marco Tezzele and Gianluigi Rozza} } @article {2021, title = {A Monolithic and a Partitioned, Reduced Basis Method for Fluid{\textendash}Structure Interaction Problems}, journal = {Fluids}, volume = {6}, year = {2021}, pages = {229}, abstract = {

The aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid{\textendash}Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek{\textendash}Hron benchmark test case, with a fluid Reynolds number Re=100.

}, issn = {2311-5521}, doi = {10.3390/fluids6060229}, url = {https://www.mdpi.com/2311-5521/6/6/229}, author = {Monica Nonino and F. Ballarin and Gianluigi Rozza} } @conference {romor2020pamm, title = {Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces}, booktitle = {Proceedings in Applied Mathematics \& Mechanics}, volume = {20}, number = {S1}, year = {2021}, publisher = {Wiley Online Library}, organization = {Wiley Online Library}, doi = {10.1002/pamm.202000349}, author = {Francesco Romor and Marco Tezzele and Gianluigi Rozza} } @article {14318, title = {Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering}, journal = {arXiv preprint arXiv:2110.14396}, year = {2021}, author = {Francesco Romor and Marco Tezzele and Markus Mrosek and Carsten Othmer and Gianluigi Rozza} } @booklet {PapapiccoDemoGirfoglioStabileRozza2021, title = {The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations}, year = {2021}, author = {Davide Papapicco and Nicola Demo and Michele Girfoglio and Giovanni Stabile and Gianluigi Rozza} } @article {2021, title = {Non-intrusive data-driven ROM framework for hemodynamics problems}, journal = {Acta Mechanica Sinica}, volume = {37}, year = {2021}, pages = {1183{\textendash}1191}, author = {Michele Girfoglio and Leonardo Scandurra and Francesco Ballarin and Giuseppe Infantino and Francesca Nicol{\`o} and Andrea Montalto and Gianluigi Rozza and Roberto Scrofani and Marina Comisso and Francesco Musumeci} } @article {StarStabileBelloniRozzaDegroote2019, title = {A novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems}, journal = {Communications in Computational Physics}, volume = {30}, number = {1}, year = {2021}, pages = {34{\textendash}66}, publisher = {Global Science Press}, abstract = {A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation. The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case.}, doi = {https://doi.org/10.4208/cicp.OA-2020-0059}, author = {Kelbij Star and Giovanni Stabile and Francesco Belloni and Gianluigi Rozza and Joris Degroote} } @article {MorelliBarralQuintelaRozzaStabile2021, title = {A numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation}, journal = {International Journal for Numerical Methods in Engineering}, volume = {122}, number = {17}, year = {2021}, pages = {4541{\textendash}4574}, publisher = {Wiley}, doi = {10.1002/nme.6713}, url = {https://doi.org/10.1002/nme.6713}, author = {Umberto Emil Morelli and Patricia Barral and Peregrina Quintela and Gianluigi Rozza and Giovanni Stabile} } @article {2021, title = {A POD-Galerkin reduced order model for a LES filtering approach}, journal = {Journal of Computational Physics}, volume = {436}, year = {2021}, abstract = {

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for an implementation of the Leray model that combines a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0<=Re<=100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.

}, doi = {10.1016/j.jcp.2021.110260}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85102138957\&doi=10.1016\%2fj.jcp.2021.110260\&partnerID=40\&md5=73115708267e80754f343561c26f4744}, author = {Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza} } @article {2021, title = {A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step}, journal = {Applied Mathematical Modelling}, volume = {89}, year = {2021}, pages = {486-503}, abstract = {

A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier{\textendash}Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 105 times faster than the RANS simulations that are performed on eight cores.

}, doi = {10.1016/j.apm.2020.07.029}, author = {Kelbij Star and Giovanni Stabile and Gianluigi Rozza and Joris Degroote} } @article {tezzele2020pygem, title = {PyGeM: Python Geometrical Morphing}, journal = {Software Impacts}, volume = {7}, year = {2021}, pages = {100047}, abstract = {PyGeM is an open source Python package which allows to easily parametrize and deform 3D object described by CAD files or 3D meshes. It implements several morphing techniques such as free form deformation, radial basis function interpolation, and inverse distance weighting. Due to its versatility in dealing with different file formats it is particularly suited for researchers and practitioners both in academia and in industry interested in computational engineering simulations and optimization studies.}, keywords = {Free form deformation, Geometrical morphing, Inverse distance weighting, Python, Radial basis functions interpolation}, issn = {2665-9638}, doi = {10.1016/j.simpa.2020.100047}, author = {Marco Tezzele and Nicola Demo and Andrea Mola and Gianluigi Rozza} } @article {2021, title = {A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier{\textendash}Stokes problems}, journal = {Computer \& Mathematics With Applications}, year = {2021}, month = {2021/08/12/}, abstract = {

We focus on steady and unsteady Navier{\textendash}Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1], [2], [3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.

}, keywords = {Cut Finite Element Method, Navier{\textendash}Stokes equations, Parameter{\textendash}dependent shape geometry, Reduced Order Models, Unfitted mesh}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122121002790}, author = {Efthymios N Karatzas and Monica Nonino and F. Ballarin and Gianluigi Rozza} } @conference { 20.500.11767_123375, title = {Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, volume = {139}, year = {2021}, pages = {841{\textendash}850}, publisher = {Springer}, organization = {Springer}, isbn = {978-3-030-55873-4}, doi = {10.1007/978-3-030-55874-1_83}, url = {https://arxiv.org/abs/1912.07886}, author = {Maria Strazzullo and Zakia Zainib and F. Ballarin and Gianluigi Rozza} } @conference {2021, title = {Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, year = {2021}, month = {2021//}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.

}, isbn = {978-3-030-55874-1}, doi = {https://doi.org/10.1007/978-3-030-55874-1_83}, url = {https://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676}, author = {Maria Strazzullo and Zakia Zainib and F. Ballarin and Gianluigi Rozza}, editor = {Fred J Vermolen and Cornelis Vuik} } @article {StarSanderseStabileRozzaDegroote2020, title = {Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a {\textquoteleft}discretize-then-project{\textquoteright} approach}, journal = {International Journal for Numerical Methods in Fluids}, volume = {93}, number = {8}, year = {2021}, pages = {2694{\textendash}2722}, publisher = {Wiley}, doi = {10.1002/fld.4994}, url = {https://doi.org/10.1002/fld.4994}, author = {Kelbij Star and Benjamin Sanderse and Giovanni Stabile and Gianluigi Rozza and Joris Degroote} } @article {2020, title = {A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems}, journal = {SIAM Journal on Scientific Computing}, volume = {43}, year = {2021}, chapter = {B831}, abstract = {

In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions {\textendash} Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov {\textendash} and finally we apply it to an aeronautical shape optimization problem.

}, doi = {https://doi.org/10.1137/20M1345219}, url = {https://arxiv.org/abs/2006.07282}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @article {2021, title = {A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers}, volume = {60}, year = {2021}, month = {2021/08/03}, pages = {191}, abstract = {

We study the approximation of finite-dimensional rate-independent quasistatic systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamic solutions to a rate-independent one, employing the variational concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.

}, isbn = {1432-0835}, url = {https://doi.org/10.1007/s00526-021-02067-6}, author = {Paolo Gidoni and Filippo Riva} } @article {2021, title = {A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences}, journal = {Computers and Mathematics with Applications}, volume = {102}, year = {2021}, pages = {261-276}, doi = {10.1016/j.camwa.2021.10.020}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561\&doi=10.1016\%2fj.camwa.2021.10.020\&partnerID=40\&md5=cb57d59a6975a35315b2cf5d0e3a6001}, author = {G. Carere and Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza and R. Stevenson} } @conference {2020, title = {Advances in reduced order methods for parametric industrial problems in computational fluid dynamics}, booktitle = {Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018}, year = {2020}, abstract = {

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686\&partnerID=40\&md5=fb0b1a3cfdfd35a104db9921bc9be675}, author = {Gianluigi Rozza and M.H. Malik and Nicola Demo and Marco Tezzele and Michele Girfoglio and Giovanni Stabile and Andrea Mola} } @article {2020, title = {On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity}, volume = {30}, year = {2020}, month = {2020/06/01}, pages = {903 - 951}, abstract = {

In this paper, we contribute to studying the issue of quasistatic limit in the context of Griffith{\textquoteright}s theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking viscosity into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.

}, isbn = {1432-1467}, url = {https://doi.org/10.1007/s00332-019-09595-8}, author = {Filippo Riva} } @inbook {RozzaHessStabileTezzeleBallarin2020, title = {Basic ideas and tools for projection-based model reduction of parametric partial differential equations}, booktitle = {Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms}, year = {2020}, pages = {1 - 47}, publisher = {De Gruyter}, organization = {De Gruyter}, address = {Berlin, Boston}, isbn = {9783110671490}, doi = {https://doi.org/10.1515/9783110671490-001}, url = {https://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml}, author = {Gianluigi Rozza and Martin W. Hess and Giovanni Stabile and Marco Tezzele and F. Ballarin} } @article {StabileRosic2020, title = {Bayesian identification of a projection-based reduced order model for computational fluid dynamics}, journal = {Computers \& Fluids}, volume = {201}, year = {2020}, pages = {104477}, abstract = {In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.}, issn = {0045-7930}, doi = {https://doi.org/10.1016/j.compfluid.2020.104477}, author = {Giovanni Stabile and Bojana Rosic} } @article {2020, title = {Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height}, journal = {Computers and Mathematics with Applications}, volume = {80}, year = {2020}, pages = {973-989}, abstract = {

In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that lets us obtain an affine decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi{\textendash}Rappaz{\textendash}Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.

}, doi = {10.1016/j.camwa.2020.05.013}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368\&doi=10.1016\%2fj.camwa.2020.05.013\&partnerID=40\&md5=7c6596865ec89651319c7dd97159dd77}, author = {F. Ballarin and Rebollo, T.C. and E.D. {\'A}vila and Marmol, M.G. and Gianluigi Rozza} } @article {2020, title = {Data-driven POD-Galerkin reduced order model for turbulent flows}, journal = {Journal of Computational Physics}, volume = {416}, year = {2020}, pages = {109513}, abstract = {

In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

}, doi = {10.1016/j.jcp.2020.109513}, url = {https://arxiv.org/abs/1907.09909}, author = {Saddam Hijazi and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @article {ArndtBangerthBlais-2020-a, title = {The deal.II library, Version 9.2}, journal = {Journal of Numerical Mathematics}, volume = {28}, number = {3}, year = {2020}, pages = {131{\textendash}146}, author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Thomas C. Clevenger and Marc Fehling and Alexander V. Grayver and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Reza Rastak and Ignacio Tomas and Bruno Turcksin and Zhuoran Wang and David Wells} } @article {13850, title = {Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method}, journal = {Advances in Computational Mathematics}, year = {2020}, abstract = {

The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

}, url = {https://arxiv.org/abs/1912.06089}, author = {Moreno Pintore and Federico Pichi and Martin W. Hess and Gianluigi Rozza and Claudio Canuto} } @article {2020, title = {Efficient Geometrical parametrization for finite-volume based reduced order methods}, journal = {International Journal for Numerical Methods in Engineering}, volume = {121}, year = {2020}, pages = {2655-2682}, abstract = {

In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier{\textendash}Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

}, doi = {10.1002/nme.6324}, url = {https://arxiv.org/abs/1901.06373}, author = {Giovanni Stabile and Matteo Zancanaro and Gianluigi Rozza} } @conference {HijaziAliStabileBallarinRozza2020, title = {The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows}, booktitle = {Lecture Notes in Computational Science and Engineering}, year = {2020}, pages = {245{\textendash}264}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

}, isbn = {978-3-030-30705-9}, doi = {10.1007/978-3-030-30705-9_22}, author = {Saddam Hijazi and Shafqat Ali and Giovanni Stabile and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {Enhancing CFD predictions in shape design problems by model and parameter space reduction}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {7}, year = {2020}, abstract = {

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

}, doi = {https://doi.org/10.1186/s40323-020-00177-y}, url = {https://arxiv.org/abs/2001.05237}, author = {Marco Tezzele and Nicola Demo and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @article {Bonelli:2020xps, title = {Gauge theories on compact toric manifolds}, year = {2020}, month = {7}, doi = {10.1007/s11005-021-01419-9}, author = {Giulio Bonelli and Francesco Fucito and Morales, Jose Francisco and Massimiliano Ronzani and Sysoeva, Ekaterina and Alessandro Tanzini} } @article {2020, title = {A hybrid reduced order method for modelling turbulent heat transfer problems}, journal = {Computers \& Fluids}, volume = {208}, year = {2020}, pages = {104615}, abstract = {

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

}, doi = {10.1016/j.compfluid.2020.104615}, url = {https://arxiv.org/abs/1906.08725}, author = {Sokratia Georgaka and Giovanni Stabile and Kelbij Star and Gianluigi Rozza and Michael J. Bluck} } @book {2020, title = {Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method}, year = {2020}, author = {Francesco Romor and Marco Tezzele and Lario, Andrea and Gianluigi Rozza} } @booklet {2020, title = {MicroROM: An Efficient and Accurate Reduced Order Method to Solve Many-Query Problems in Micro-Motility}, year = {2020}, keywords = {FOS: Mathematics, Numerical Analysis (math.NA)}, doi = {10.48550/ARXIV.2006.13836}, url = {https://arxiv.org/abs/2006.13836}, author = {Nicola Giuliani and Martin W. Hess and Antonio DeSimone and Gianluigi Rozza} } @inbook {HijaziStabileMolaRozza2020a, title = {Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives}, booktitle = {Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions}, year = {2020}, pages = {217{\textendash}240}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

}, isbn = {978-3-030-48721-8}, doi = {10.1007/978-3-030-48721-8_10}, url = {https://doi.org/10.1007/978-3-030-48721-8_10}, author = {Saddam Hijazi and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @unpublished {2020, title = {POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations}, year = {2020}, abstract = {

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

}, author = {Maria Strazzullo and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {POD{\textendash}Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation}, journal = {Journal of Scientific Computing}, volume = {83}, year = {2020}, abstract = {

In this work we deal with parametrized time dependent optimal control problems governed by partial differential equations. We aim at extending the standard saddle point framework of steady constraints to time dependent cases. We provide an analysis of the well-posedness of this formulation both for parametrized scalar parabolic constraint and Stokes governing equations and we propose reduced order methods as an effective strategy to solve them. Indeed, on one hand, parametrized time dependent optimal control is a very powerful mathematical model which is able to describe several physical phenomena, on the other, it requires a huge computational effort. Reduced order methods are a suitable approach to have rapid and accurate simulations. We rely on POD{\textendash}Galerkin reduction over the physical and geometrical parameters of the optimality system in a space-time formulation. Our theoretical results and our methodology are tested on two examples: a boundary time dependent optimal control for a Graetz flow and a distributed optimal control governed by time dependent Stokes equations. With these two test cases the convenience of the reduced order modelling is further extended to the field of time dependent optimal control.

}, doi = {10.1007/s10915-020-01232-x}, author = {Maria Strazzullo and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {POD{\textendash}Galerkin reduced order methods for combined Navier{\textendash}Stokes transport equations based on a hybrid FV-FE solver}, journal = {Computers and Mathematics with Applications}, volume = {79}, year = {2020}, pages = {256-273}, abstract = {

The purpose of this work is to introduce a novel POD{\textendash}Galerkin strategy for the semi-implicit hybrid high order finite volume/finite element solver introduced in Berm{\'u}dez et al. (2014) and Busto et al. (2018). The interest is into the incompressible Navier{\textendash}Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.

}, doi = {10.1016/j.camwa.2019.06.026}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567\&doi=10.1016\%2fj.camwa.2019.06.026\&partnerID=40\&md5=a8dcce1b53b8ee872d174bbc4c20caa3}, author = {S. Busto and Giovanni Stabile and Gianluigi Rozza and M.E. V{\'a}zquez-Cend{\'o}n} } @article {2020, title = {Projection-based reduced order models for a cut finite element method in parametrized domains}, journal = {Computers and Mathematics with Applications}, volume = {79}, year = {2020}, pages = {833-851}, abstract = {

This work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail.

}, doi = {10.1016/j.camwa.2019.08.003}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85070900852\&doi=10.1016\%2fj.camwa.2019.08.003\&partnerID=40\&md5=2d222ab9c7832955d155655d3c93e1b1}, author = {Efthymios N Karatzas and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {Reduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature}, journal = {International Journal of Computational Fluid Dynamics}, volume = {34}, year = {2020}, pages = {119-126}, abstract = {

We consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

}, doi = {10.1080/10618562.2019.1645328}, url = {https://arxiv.org/abs/1901.03708}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @article {2020, title = {Reduced basis model order reduction for Navier{\textendash}Stokes equations in domains with walls of varying curvature}, journal = {International Journal of Computational Fluid Dynamics}, volume = {34}, year = {2020}, pages = {119-126}, abstract = {

We consider the Navier{\textendash}Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced-order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced-order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e. symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

}, doi = {10.1080/10618562.2019.1645328}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085233294\&doi=10.1080\%2f10618562.2019.1645328\&partnerID=40\&md5=e2ed8f24c66376cdc8b5485aa400efb0}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @conference {2020, title = {A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries}, booktitle = {IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22{\textendash}25, 2018}, year = {2020}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, abstract = {

A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

}, doi = {10.1007/978-3-030-21013-7_8}, url = {https://arxiv.org/abs/1807.07753}, author = {Efthymios N Karatzas and Giovanni Stabile and Nabib Atallah and Guglielmo Scovazzi and Gianluigi Rozza}, editor = {Fehr, J{\"o}rg and Bernard Haasdonk} } @article {2020, title = {Reduced order isogeometric analysis approach for pdes in parametrized domains}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {137}, year = {2020}, pages = {153-170}, abstract = {

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

}, doi = {10.1007/978-3-030-48721-8_7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035\&doi=10.1007\%2f978-3-030-48721-8_7\&partnerID=40\&md5=7b15836ae65fa28dcfe8733788d7730c}, author = {Fabrizio Garotta and Nicola Demo and Marco Tezzele and Massimo Carraturo and Alessandro Reali and Gianluigi Rozza} } @article {2020, title = {Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation}, journal = {International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng}, volume = {n/a}, year = {2020}, month = {2020/05/27}, pages = {e3367}, abstract = {

Abstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

}, keywords = {coronary artery bypass grafts, data assimilation, flow control, Galerkin methods, hemodynamics modeling, Optimization, patient-specific simulations, Proper orthogonal decomposition, reduced order methods}, isbn = {2040-7939}, doi = {https://doi.org/10.1002/cnm.3367}, url = {https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R}, author = {Zakia Zainib and F. Ballarin and Stephen E. Fremes and Piero Triverio and Laura Jim{\'e}nez-Juan and Gianluigi Rozza} } @article {2020, title = {A reduced order modeling technique to study bifurcating phenomena: Application to the gross-pitaevskii equation}, journal = {SIAM Journal on Scientific Computing}, year = {2020}, abstract = {

We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton{\textquoteright}s method with a reduced order modeling (ROM) technique, suitably supplemented with a hyperreduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schr{\"o}dinger equation, called the Gross{Pitaevskii equation, as one or two physical parameters are varied. In the two-parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard full order method.

}, doi = {10.1137/20M1313106}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85096768803\&doi=10.1137\%2f20M1313106\&partnerID=40\&md5=47d6012d10854c2f9a04b9737f870592}, author = {Federico Pichi and Annalisa Quaini and Gianluigi Rozza} } @article {2020, title = {A Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation}, journal = {SIAM Journal on Scientific Computing}, year = {2020}, abstract = {

We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton{\textquoteright}s method with a Reduced Order Modeling (ROM) technique, suitably supplemented with a hyper-reduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schr{\"o}dinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied. In the two parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard Full Order Method.

}, doi = {https://doi.org/10.1137/20M1313106}, url = {https://arxiv.org/abs/1907.07082}, author = {Federico Pichi and Annalisa Quaini and Gianluigi Rozza} } @article {2020, title = {A reduced-order shifted boundary method for parametrized incompressible Navier{\textendash}Stokes equations}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {370}, year = {2020}, abstract = {

We investigate a projection-based reduced order model of the steady incompressible Navier{\textendash}Stokes equations for moderate Reynolds numbers. In particular, we construct an {\textquotedblleft}embedded{\textquotedblright} reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

}, doi = {10.1016/j.cma.2020.113273}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522\&doi=10.1016\%2fj.cma.2020.113273\&partnerID=40\&md5=d864e4808190b682ecb1c8b27cda72d8}, author = {Efthymios N Karatzas and Giovanni Stabile and Leo Nouveau and Guglielmo Scovazzi and Gianluigi Rozza} } @article {2020, title = {Special Issue on Reduced Order Models in CFD}, journal = {International Journal of Computational Fluid Dynamics}, volume = {34}, year = {2020}, pages = {91-92}, doi = {10.1080/10618562.2020.1756497}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084258805\&doi=10.1080\%2f10618562.2020.1756497\&partnerID=40\&md5=d9316aad9ba95f244e07379318ebbcba}, author = {Simona Perotto and Gianluigi Rozza} } @article {2020, title = {A spectral element reduced basis method for navier{\textendash}stokes equations with geometric variations}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {134}, year = {2020}, pages = {561-571}, abstract = {

We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

}, doi = {10.1007/978-3-030-39647-3_45}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @article {2020, title = {Stabilized reduced basis methods for parametrized steady Stokes and Navier{\textendash}Stokes equations}, journal = {Computers and Mathematics with Applications}, volume = {80}, year = {2020}, pages = {2399-2416}, abstract = {

It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf{\textendash}sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf{\textendash}sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf{\textendash}sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi{\textendash}Pitkaranta, Franca{\textendash}Hughes, streamline upwind Petrov{\textendash}Galerkin, Galerkin Least Square. In the spirit of offline{\textendash}online reduced basis computational splitting, two such options are proposed, namely offline-only stabilization and offline{\textendash}online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf{\textendash}sup stability is still preserved at the reduced order level.

}, doi = {10.1016/j.camwa.2020.03.019}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083340115\&doi=10.1016\%2fj.camwa.2020.03.019\&partnerID=40\&md5=7ace96eee080701acb04d8155008dd7d}, author = {Shafqat Ali and F. Ballarin and Gianluigi Rozza} } @article {RICCOBELLI2020103745, title = {Surface tension controls the onset of gyrification in brain organoids}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {134}, year = {2020}, pages = {103745}, abstract = {

Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e.\ the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

}, keywords = {Buckling, Embryogenesis, Morpho-elasticity, Post-buckling analysis, Surface tension}, issn = {0022-5096}, doi = {https://doi.org/10.1016/j.jmps.2019.103745}, url = {http://www.sciencedirect.com/science/article/pii/S0022509619304065}, author = {Davide Riccobelli and Giulia Bevilacqua} } @article {riccobelli2018activation, title = {Activation of a muscle as a mapping of stress{\textendash}strain curves}, journal = {Extreme Mech. Lett.}, volume = {28}, year = {2019}, pages = {37{\textendash}42}, publisher = {Elsevier BV}, author = {Davide Riccobelli and D. Ambrosi} } @article {gadalla19bladex, title = {BladeX: Python Blade Morphing}, journal = {The Journal of Open Source Software}, volume = {4}, number = {34}, year = {2019}, pages = {1203}, doi = {10.21105/joss.01203}, author = {Mahmoud Gadalla and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry {\textemdash} assuming the topology is inaltered by the deformation {\textemdash}, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565\&partnerID=40\&md5=d76b8a1290053e7a84fb8801c0e6bb3d}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {VIII International Conference on Computational Methods in Marine Engineering}, year = {2019}, abstract = {

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry {\textendash}- assuming the topology is inaltered by the deformation {\textendash}-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

}, url = {https://arxiv.org/abs/1905.05982}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {2019, title = {A continuous dependence result for a dynamic debonding model in dimension one}, number = {SISSA;05/2019/MATE}, year = {2019}, institution = {SISSA}, abstract = {

In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith{\textquoteright}s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35329}, author = {Filippo Riva} } @conference {2019, title = {Efficient reduction in shape parameter space dimension for ship propeller blade design}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143\&partnerID=40\&md5=b6aa0fcedc2f88e78c295d0f437824d0}, author = {Andrea Mola and Marco Tezzele and Mahmoud Gadalla and Valdenazzi, Federica and Grassi, Davide and Padovan, Roberta and Gianluigi Rozza} } @article {GENTIL2019, title = {An entropic interpolation proof of the HWI inequality}, journal = {Stochastic Processes and their Applications}, year = {2019}, abstract = {

The HWI inequality is an {\textquotedblleft}interpolation{\textquotedblright}inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schr{\"o}dinger problem. Our approach consists in making rigorous the Otto{\textendash}Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

}, keywords = {Entropic interpolations, Fisher information, Relative entropy, Schr{\"o}dinger problem, Wasserstein distance}, issn = {0304-4149}, doi = {https://doi.org/10.1016/j.spa.2019.04.002}, url = {http://www.sciencedirect.com/science/article/pii/S0304414918303454}, author = {Ivan Gentil and Christian L{\'e}onard and Luigia Ripani and Luca Tamanini} } @article {HeltaiRotundo-2019-a, title = {Error estimates in weighted Sobolev norms for finite element immersed interface methods}, journal = {Computers \& Mathematics with Applications}, volume = {78}, number = {11}, year = {2019}, pages = {3586{\textendash}3604}, publisher = {Elsevier BV}, doi = {10.1016/j.camwa.2019.05.029}, url = {https://doi.org/10.1016/j.camwa.2019.05.029}, author = {Luca Heltai and Nella Rotundo} } @article {riccobelli2018constitutive, title = {On the existence of elastic minimizers for initially stressed materials}, journal = {Phil. Trans. R. Soc. A}, volume = {377}, number = {2144}, year = {2019}, publisher = {The Royal Society}, author = {Davide Riccobelli and A. Agosti and Pasquale Ciarletta} } @article {2019, title = {A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization}, journal = {Computers and Fluids}, volume = {187}, year = {2019}, pages = {27-45}, abstract = {

We consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method. Our approach is validated against numerical data available in the literature for the 2D flow past a cylinder and against experimental measurements for the 3D fluid flow in an idealized medical device, as recommended by the U.S. Food and Drug Administration. We will show that for similar levels of mesh refinement FV and FE methods provide significantly different results. Through our numerical experiments, we are able to provide practical directions to tune the parameters involved in EFR algorithm. Furthermore, we are able to investigate the impact of mesh features (element type, non-orthogonality, local refinement, and element aspect ratio) and the discretization method for the convective term on the agreement between numerical solutions and experimental data.

}, doi = {10.1016/j.compfluid.2019.05.001}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85065471890\&doi=10.1016\%2fj.compfluid.2019.05.001\&partnerID=40\&md5=c982371b5b5d4b5664a676902aaa60f4}, author = {Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza} } @article {2019, title = {A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization}, journal = {Computers \& Fluids}, volume = {187}, year = {2019}, pages = {27-45}, abstract = {

We consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method. Our approach is validated against numerical data available in the literature for the 2D flow past a cylinder and against experimental measurements for the 3D fluid flow in an idealized medical device, as recommended by the U.S. Food and Drug Administration. We will show that for similar levels of mesh refinement FV and FE methods provide significantly different results. Through our numerical experiments, we are able to provide practical directions to tune the parameters involved in the model. Furthermore, we are able to investigate the impact of mesh features (element type, non-orthogonality, local refinement, and element aspect ratio) and the discretization method for the convective term on the agreement between numerical solutions and experimental data.

}, doi = {10.1016/j.compfluid.2019.05.001}, url = {https://arxiv.org/abs/1901.05251}, author = {Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza} } @article {2019, title = {A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {351}, year = {2019}, pages = {379-403}, abstract = {

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

}, doi = {10.1016/j.cma.2019.03.050}, url = {https://arxiv.org/abs/1807.08851}, author = {Martin W. Hess and Alla, Alessandro and Annalisa Quaini and Gianluigi Rozza and Max Gunzburger} } @article {2019, title = {A localized reduced-order modeling approach for PDEs with bifurcating solutions}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {351}, year = {2019}, pages = {379-403}, abstract = {

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. Although ROMs have been successfully used in many settings, ROMs built specifically for the efficient treatment of PDEs having solutions that bifurcate as the values of input parameters change have not received much attention. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does not respect the often large differences in the PDE solutions corresponding to different subregions. In this work, we develop and test a new ROM approach specifically aimed at bifurcation problems. In the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

}, doi = {10.1016/j.cma.2019.03.050}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85064313505\&doi=10.1016\%2fj.cma.2019.03.050\&partnerID=40\&md5=8b095034b9e539995facc7ce7bafa9e9}, author = {Martin W. Hess and Alla, Alessandro and Annalisa Quaini and Gianluigi Rozza and Max Gunzburger} } @article {2019, title = {A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces}, journal = {Comptes Rendus - Mecanique}, volume = {347}, year = {2019}, pages = {873-881}, abstract = {

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions{\textemdash}computed for properly chosen parameters, using a full-order model{\textemdash}in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI){\textemdash}a data-driven reduced order method{\textemdash}with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one.

}, doi = {https://doi.org/10.1016/j.crme.2019.11.012}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471\&doi=10.1016\%2fj.crme.2019.11.012\&partnerID=40\&md5=dcb27af39dc14dc8c3a4a5f681f7d84b}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @article {gigli_rigoni_2019, title = {A Note About the Strong Maximum Principle on RCD Spaces}, journal = {Canadian Mathematical Bulletin}, volume = {62}, number = {2}, year = {2019}, pages = {259{\textendash}266}, publisher = {Canadian Mathematical Society}, abstract = {

We give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

}, doi = {10.4153/CMB-2018-022-9}, author = {Nicola Gigli and Chiara Rigoni} } @article {2019, title = {Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems}, journal = {Communications in Computational Physics}, volume = {27}, year = {2019}, pages = {1{\textendash}32}, abstract = {

A parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

}, issn = {1991-7120}, doi = {10.4208/cicp.OA-2018-0207}, url = {https://arxiv.org/abs/1808.05175}, author = {Sokratia Georgaka and Giovanni Stabile and Gianluigi Rozza and Michael J. Bluck} } @conference {StarStabileGeorgakaBelloniRozzaDegroote2019, title = {POD-Galerkin Reduced Order Model of the Boussinesq Approximation for Buoyancy-Driven Enclosed Flows}, booktitle = {International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019}, year = {2019}, isbn = {9780894487699}, author = {Kelbij Star and Giovanni Stabile and Sokratia Georgaka and Francesco Belloni and Gianluigi Rozza and Joris Degroote} } @article {2019, title = {A POD-selective inverse distance weighting method for fast parametrized shape morphing}, journal = {International Journal for Numerical Methods in Engineering}, volume = {117}, year = {2019}, pages = {860-884}, abstract = {

Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.

}, doi = {10.1002/nme.5982}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233\&doi=10.1002\%2fnme.5982\&partnerID=40\&md5=6aabcbdc9a0da25e36575a0ebfac034f}, author = {F. Ballarin and A. D{\textquoteright}Amario and Simona Perotto and Gianluigi Rozza} } @article {2019, title = {A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {347}, year = {2019}, pages = {568-587}, abstract = {

We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM. This unfitted boundary method permits to avoid remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is reduced by the development of a Reduced Order Model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.

}, doi = {10.1016/j.cma.2018.12.040}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322\&doi=10.1016\%2fj.cma.2018.12.040\&partnerID=40\&md5=1a3234f0cb000c91494d946428f8ebef}, author = {Efthymios N Karatzas and Giovanni Stabile and Leo Nouveau and Guglielmo Scovazzi and Gianluigi Rozza} } @article {2019, title = {Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von K{\'a}rm{\'a}n Equations}, journal = {Journal of Scientific Computing}, volume = {81}, year = {2019}, pages = {112-135}, abstract = {

This work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von K{\'a}rm{\'a}n plate equations based on reduced order methods and spectral analysis. The computational complexity{\textemdash}due to the fourth order derivative terms, the non-linearity and the parameter dependence{\textemdash}provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode.

}, doi = {10.1007/s10915-019-01003-3}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068973907\&doi=10.1007\%2fs10915-019-01003-3\&partnerID=40\&md5=a09af83ce45183d6965cdb79d87a919b}, author = {Federico Pichi and Gianluigi Rozza} } @article {2019, title = {Reduced basis approaches for parametrized bifurcation problems held by non-linear Von K{\'a}rm{\'a}n equations}, volume = {81}, year = {2019}, pages = {112{\textendash}135}, abstract = {

This work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von K{\'a}rm{\'a}n plate equations based on reduced order methods and spectral analysis. The computational complexity - due to the fourth order derivative terms, the non-linearity and the parameter dependence - provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode. journal = Journal of Scientific Computing

}, doi = {10.1007/s10915-019-01003-3}, url = {https://arxiv.org/abs/1804.02014}, author = {Federico Pichi and Gianluigi Rozza} } @article {2019, title = {A reduced order variational multiscale approach for turbulent flows}, journal = {Advances in Computational Mathematics}, volume = {45}, year = {2019}, pages = {2349-2368}, abstract = {

The purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.

}, doi = {10.1007/s10444-019-09712-x}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665\&doi=10.1007\%2fs10444-019-09712-x\&partnerID=40\&md5=af0142e6d13bbc2e88c6f31750aef6ad}, author = {Giovanni Stabile and F. Ballarin and G. Zuccarino and Gianluigi Rozza} } @conference {2019, title = {Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244\&partnerID=40\&md5=3e1f2e9a2539d34594caff13766c94b8}, author = {Marco Tezzele and Nicola Demo and Gianluigi Rozza} } @inbook {2019, title = {A Spectral Element Reduced Basis Method in Parametric CFD}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, volume = {126}, year = {2019}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, chapter = {A Spectral Element Reduced Basis Method in Parametric CFD}, abstract = {

We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

}, doi = {10.1007/978-3-319-96415-7_64 pages = 693{\textendash}701}, url = {https://arxiv.org/abs/1712.06432}, author = {Martin W. Hess and Gianluigi Rozza}, editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin} } @article {2019, title = {A spectral element reduced basis method in parametric CFD}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {126}, year = {2019}, pages = {693-701}, abstract = {

We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot solutions define a reduced order space, which allows to accurately evaluate the steady-state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

}, doi = {10.1007/978-3-319-96415-7_64}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060005503\&doi=10.1007\%2f978-3-319-96415-7_64\&partnerID=40\&md5=d1a900db8ddb92cd818d797ec212a4c6}, author = {Martin W. Hess and Gianluigi Rozza} } @article {2019, title = {A Weighted POD Method for Elliptic PDEs with Random Inputs}, journal = {Journal of Scientific Computing}, volume = {81}, year = {2019}, pages = {136-153}, abstract = {

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems. The algorithm is introduced alongside the weighted greedy method. Our proposed method aims to minimize the error in a L2 norm and, in contrast to the weighted greedy approach, it does not require the availability of an error bound. Moreover, we consider sparse discretization of the input space in the construction of the reduced model; for high-dimensional problems, provided the sampling is done accordingly to the parameters distribution, this enables a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We provide many numerical tests to assess the performance of the proposed method compared to an equivalent reduced order model without weighting, as well as to the weighted greedy approach, in both low and high dimensional problems.

}, doi = {10.1007/s10915-018-0830-7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053798049\&doi=10.1007\%2fs10915-018-0830-7\&partnerID=40\&md5=5cad501b6ef1955da55868807079ee5d}, author = {L.Venturi and F. Ballarin and Gianluigi Rozza} } @article {2019, title = {Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs}, journal = {PoliTO Springer Series}, year = {2019}, pages = {27-40}, abstract = {

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.

}, doi = {10.1007/978-3-030-04870-9_2}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379\&doi=10.1007\%2f978-3-030-04870-9_2\&partnerID=40\&md5=446bcc1f331167bbba67bc00fb170150}, author = {L. Venturi and D. Torlo and F. Ballarin and Gianluigi Rozza} } @article {20.500.11767_81647, title = {An authenticated theoretical modeling of electrified fluid jet in core{\textendash}shell nanofibers production}, journal = {JOURNAL OF INDUSTRIAL TEXTILES}, volume = {47}, year = {2018}, pages = {1791{\textendash}1811}, doi = {10.1177/1528083717710711}, author = {Rafiei, S. and Noroozi, B. and Luca Heltai and Haghi, A. K.} } @article {2018, title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models}, journal = {Journal of Scientific Computing}, volume = {74}, year = {2018}, pages = {197-219}, doi = {10.1007/s10915-017-0430-y}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114\&doi=10.1007\%2fs10915-017-0430-y\&partnerID=40\&md5=023ef0bb95713f4442d1fa374c92a964}, author = {Immanuel Martini and Bernard Haasdonk and Gianluigi Rozza} } @inbook {tezzele2018combined, title = {Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods}, booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications}, year = {2018}, pages = {185{\textendash}207}, publisher = {Springer}, organization = {Springer}, author = {Marco Tezzele and F. Ballarin and Gianluigi Rozza} } @article {giantesio2017comparison, title = {A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials}, journal = {J. Elast.}, year = {2018}, publisher = {Springer Nature}, author = {Giulia Giantesio and Alessandro Musesti and Davide Riccobelli} } @inbook {AuricchioContiLefieuxMorgantiRealiRozzaVeneziani2018, title = {Computational methods in cardiovascular mechanics}, booktitle = {Cardiovascular Mechanics}, year = {2018}, pages = {54}, publisher = {CRC Press}, organization = {CRC Press}, chapter = {Computational methods in cardiovascular mechanics}, abstract = {

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

}, url = {https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201\%2Fb21917-5}, author = {Auricchio, Ferdinando and Conti, Michele and Lefieux, Adrian and Morganti, Simone and Alessandro Reali and Gianluigi Rozza and Veneziani, Alessandro}, editor = {Michel F. Labrosse} } @article {TezzeleSalmoiraghiMolaRozza2018, title = {Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {5}, number = {1}, year = {2018}, month = {Sep}, pages = {25}, abstract = {

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

}, doi = {10.1186/s40323-018-0118-3}, author = {Marco Tezzele and Filippo Salmoiraghi and Andrea Mola and Gianluigi Rozza} } @proceedings {demo2018efficient, title = {An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment}, year = {2018}, publisher = {International Society of Offshore and Polar Engineers}, address = {Sapporo, Japan}, abstract = {In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.}, keywords = {Active subspaces, Boundary element method, Dynamic mode decomposition, Fluid structure interaction, Free form deformation, Fully nonlinear potential, Numerical towing tank}, issn = {978-1-880653-87-6}, url = {https://www.onepetro.org/conference-paper/ISOPE-I-18-481}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {2018, title = {Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping}, number = {SISSA;28/2018/MATE}, year = {2018}, abstract = {

In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth{\textquoteright}s criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth{\textquoteright}s criterion.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35319}, author = {Lorenzo Nardini and Filippo Riva} } @article {demo2018ezyrb, title = {EZyRB: Easy Reduced Basis method}, journal = {The Journal of Open Source Software}, volume = {3}, number = {24}, year = {2018}, pages = {661}, doi = {10.21105/joss.00661}, url = {https://joss.theoj.org/papers/10.21105/joss.00661}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @inbook {Bianchini2018, title = {Failure of the Chain Rule in the Non Steady Two-Dimensional Setting}, booktitle = {Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg}, year = {2018}, pages = {33{\textendash}60}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-89800-1}, doi = {10.1007/978-3-319-89800-1_2}, url = {https://doi.org/10.1007/978-3-319-89800-1_2}, author = {Stefano Bianchini and Paolo Bonicatto}, editor = {Rassias, Themistocles M.} } @article {2018, title = {Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier{\textendash}Stokes equations}, journal = {Computers and Fluids}, volume = {173}, year = {2018}, pages = {273-284}, abstract = {

In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier{\textendash}Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a finite volumes approximation. The reduced basis spaces are constructed with a POD approach. Two different pressure stabilisation strategies are proposed and compared: the former one is based on the supremizer enrichment of the velocity space, and the latter one is based on a pressure Poisson equation approach.

}, doi = {10.1016/j.compfluid.2018.01.035}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85043366603\&doi=10.1016\%2fj.compfluid.2018.01.035\&partnerID=40\&md5=c15435ea3b632e55450da19ba2bb6125}, author = {Giovanni Stabile and Gianluigi Rozza} } @article {SalmoiraghiScardigliTelibRozza2018, title = {Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation}, journal = {International Journal of Computational Fluid Dynamics}, volume = {32}, number = {4-5}, year = {2018}, pages = {233-247}, publisher = {Taylor \& Francis}, abstract = {

In this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier{\textendash}Stokes equations.

}, doi = {10.1080/10618562.2018.1514115}, author = {Filippo Salmoiraghi and Scardigli, Angela and Telib, Haysam and Gianluigi Rozza} } @article {1806.03437, title = {Long time existence for fully nonlinear NLS with small Cauchy data on the circle}, year = {2018}, author = {Feola Roberto and Felice Iandoli} } @conference {tezzele2018model, title = {Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, address = {Trieste, Italy}, abstract = {We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.}, doi = {10.3233/978-1-61499-870-9-569}, url = {http://ebooks.iospress.nl/publication/49270}, author = {Marco Tezzele and Nicola Demo and Mahmoud Gadalla and Andrea Mola and Gianluigi Rozza} } @article {doi:10.1137/17M1150591, title = {Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering}, journal = {SIAM Journal on Scientific Computing}, volume = {40}, number = {4}, year = {2018}, pages = {B1055-B1079}, doi = {10.1137/17M1150591}, url = {https://doi.org/10.1137/17M1150591}, author = {Maria Strazzullo and F. Ballarin and Mosetti, R. and Gianluigi Rozza} } @article {riccobelli2018morpho, title = {Morpho-elastic model of the tortuous tumour vessels}, journal = {Int. J. Non-Linear Mech.}, volume = {107}, year = {2018}, pages = {1{\textendash}9}, publisher = {Elsevier BV}, author = {Davide Riccobelli and Pasquale Ciarletta} } @article {BeCaRu, title = {Noncommutative Painlev{\'e} Equations and Systems of Calogero Type}, journal = {Comm. Math. Phys}, year = {2018}, author = {Marco Bertola and Mattia Cafasso and V. Rubtsov} } @article {demo2018pydmd, title = {PyDMD: Python Dynamic Mode Decomposition}, journal = {The Journal of Open Source Software}, volume = {3}, number = {22}, year = {2018}, pages = {530}, doi = {10.21105/joss.00530}, url = {https://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @article {Gigli2018, title = {Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {57}, number = {4}, year = {2018}, month = {Jun}, pages = {104}, abstract = {

We prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

}, issn = {1432-0835}, doi = {10.1007/s00526-018-1377-z}, url = {https://doi.org/10.1007/s00526-018-1377-z}, author = {Nicola Gigli and Chiara Rigoni} } @inbook {2018, title = {Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings}, booktitle = {Numerical Methods for PDEs}, volume = {15}, number = {SEMA SIMAI}, year = {2018}, doi = {https://doi.org/10.1007/978-3-319-94676-4_8}, url = {https://link.springer.com/chapter/10.1007/978-3-319-94676-4_8}, author = {Huynh, D. B. P. and Federico Pichi and Gianluigi Rozza} } @article {2018, title = {Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings}, journal = {SEMA SIMAI Springer Series}, volume = {15}, year = {2018}, pages = {203-247}, abstract = {

In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinely parametrized geometries. The essential ingredients of the methodology are: a Galerkin projection onto a low-dimensional space associated with a smooth {\textquotedblleft}parametric manifold{\textquotedblright}{\textemdash}dimension reduction; an efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations{\textemdash}rapid convergence; an a posteriori error estimation procedures{\textemdash}rigorous and sharp bounds for the functional outputs related with the underlying solution or related quantities of interest, like stress intensity factor; and Offline-Online computational decomposition strategies{\textemdash}minimum marginal cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present several illustrative results for linear elasticity problem in parametrized geometries representing 2D Cartesian or 3D axisymmetric configurations like an arc-cantilever beam, a center crack problem, a composite unit cell or a woven composite beam, a multi-material plate, and a closed vessel. We consider different parametrization for the systems: either physical quantities{\textemdash}to model the materials and loads{\textemdash}and geometrical parameters{\textemdash}to model different geometrical configurations{\textemdash}with isotropic and orthotropic materials working in plane stress and plane strain approximation. We would like to underline the versatility of the methodology in very different problems. As last example we provide a nonlinear setting with increased complexity.

}, doi = {10.1007/978-3-319-94676-4_8}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85055036627\&doi=10.1007\%2f978-3-319-94676-4_8\&partnerID=40\&md5=e9c07038e7bcc6668ec702c0653410dc}, author = {D.B.P. Huynh and Federico Pichi and Gianluigi Rozza} } @conference {demo2018shape, title = {Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, chapter = {212}, address = {Trieste, Italy}, abstract = {Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship.}, doi = {10.3233/978-1-61499-870-9-212}, url = {http://ebooks.iospress.nl/publication/49229}, author = {Nicola Demo and Marco Tezzele and Gianluca Gustin and Gianpiero Lavini and Gianluigi Rozza} } @article {riccobelli2017shape, title = {Shape transitions in a soft incompressible sphere with residual stresses}, journal = {Math. Mech. Solids}, volume = {23}, number = {12}, year = {2018}, pages = {1507{\textendash}1524}, publisher = {SAGE Publications Sage UK: London, England}, author = {Davide Riccobelli and Pasquale Ciarletta} } @conference {2018, title = {SRTP 2.0 - The evolution of the safe return to port concept}, booktitle = {Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research}, year = {2018}, abstract = {

In 2010 IMO (International Maritime Organisation) introduced new rules in SOLAS with the aim of intrinsically increase the safety of passenger ships. This requirement is achieved by providing safe areas for passengers and essential services for allowing ship to Safely Return to Port (SRtP). The entry into force of these rules has changed the way to design passenger ships. In this respect big effort in the research has been done by industry to address design issues related to the impact on failure analysis of the complex interactions among systems. Today the research activity is working to bring operational matters in the design stage. This change of research focus was necessary because human factor and the way to operate the ship itself after a casualty on board may have a big impact in the design of the ship/systems. Also the management of the passengers after a casualty is becoming a major topic for safety. This paper presents the state of the art of Italian knowledge in the field of system engineering applied to passenger ship address to safety improvement and design reliability. An overview of present tools and methodologies will be offered together with future focuses in the research activity.

}, doi = {10.3233/978-1-61499-870-9-665}, author = {D. Cangelosi and A. Bonvicini and M. Nardo and Andrea Mola and A. Marchese and Marco Tezzele and Gianluigi Rozza} } @article {2018, title = {Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs}, journal = {SIAM-ASA Journal on Uncertainty Quantification}, volume = {6}, year = {2018}, pages = {1475-1502}, abstract = {

In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

}, doi = {10.1137/17M1163517}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502\&doi=10.1137\%2f17M1163517\&partnerID=40\&md5=6c54e2f0eb727cb85060e988486b8ac8}, author = {D. Torlo and F. Ballarin and Gianluigi Rozza} } @article {2017, title = {On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics}, journal = {Journal of Scientific Computing}, year = {2017}, abstract = {

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

}, doi = {10.1007/s10915-017-0419-6}, author = {Giuseppe Pitton and Gianluigi Rozza} } @inbook {2017, title = {Certi fied Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation}, booktitle = {Spectral and High Order Methods for Partial Differential Equations }, volume = { 119}, number = {LNCSE}, year = {2017}, publisher = {Springer}, organization = {Springer}, edition = {Bittencourt, Dumont, Hesthaven. (Eds).}, address = {Heildeberg}, abstract = {

In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization

of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis

\ (IGA) is a growing research theme in scientic computing and computational mechanics, as well as reduced

basis methods for parametric PDEs. Their combination enhances the solution of some class of problems,

especially the ones characterized by parametrized geometries we introduced in this work. For a general

overview on Reduced Basis (RB) methods we recall [7, 15] and on IGA [3]. This work wants to demonstrate

that it is also possible for some class of problems to deal with ane geometrical parametrization combined

with a NURBS IGA formulation. This is what this work brings as original ingredients with respect to other

works dealing with reduced order methods and IGA (set in a non-affine formulation, and using a POD [2]\ 

sampling without certication: see for example for potential\ flows [12] and for Stokes\ flows [17]). In this work

we show a certication of accuracy and a complete integration between IGA formulation and parametric

certified greedy RB formulation. Section 2 recalls the abstract setting for parametrized PDEs, Section 3

recalls IGA setting, Section 4 deals with RB formulation, and Section 5 illustrates two numerical examples in heat transfer with different parametrization.

}, isbn = {978-3-319-65869-8}, author = {Denis Devaud and Gianluigi Rozza} } @article {2017, title = {On a certified smagorinsky reduced basis turbulence model}, journal = {SIAM Journal on Numerical Analysis}, volume = {55}, year = {2017}, pages = {3047-3067}, doi = {10.1137/17M1118233}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218\&doi=10.1137\%2f17M1118233\&partnerID=40\&md5=221d9cd2bcc74121fcef93efd9d3d76c}, author = {Rebollo, T.C. and E.D. {\'A}vila and Marmol, M.G. and F. Ballarin and Gianluigi Rozza} } @article {RIZZI20175306, title = {Clifford Tori and the singularly perturbed Cahn{\textendash}Hilliard equation}, journal = {Journal of Differential Equations}, volume = {262}, number = {10}, year = {2017}, pages = {5306 - 5362}, abstract = {

In this paper we construct entire solutions uε to the Cahn{\textendash}Hilliard equation -ε2Δ(-ε2Δu+W'(u))+W"(u)(-ε2Δu+W'(u))=ε4λε(1-uε), under the volume constraint ∫R3(1-uε)2dx=82π2cε, with cε{\textrightarrow}1 as ε{\textrightarrow}0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε{\textrightarrow}0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov{\textendash}Schmidt reduction and on careful geometric expansions of the Laplacian.

}, keywords = {Cahn{\textendash}Hilliard equation, Clifford Torus, Lyapunov{\textendash}Schmidt reduction, Willmore surface}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2017.01.026}, url = {http://www.sciencedirect.com/science/article/pii/S0022039617300530}, author = {Matteo Rizzi} } @article {2017, title = {Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology}, journal = {Journal of Computational Physics}, volume = {344}, year = {2017}, month = {09/2017}, pages = {557}, chapter = {534}, abstract = {

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier{\textendash}Stokes equations for a Newtonian and viscous fluid in contraction{\textendash}expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

}, keywords = {Parametrized Navier{\textendash}Stokes equations, Reduced basis method, Stability of flows, Symmetry breaking bifurcation}, doi = {https://doi.org/10.1016/j.jcp.2017.05.010}, author = {Giuseppe Pitton and Annalisa Quaini and Gianluigi Rozza} } @article {BERSHTEIN201740, title = {Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants}, journal = {Journal of Geometry and Physics}, volume = {118}, year = {2017}, note = {Interactions between Geometry and Physics. A Special Issue in Honor of Ugo Bruzzo{\textquoteright}s 60th Birthday}, pages = {40 - 50}, abstract = {

We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$\ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics {\textemdash} in honor of Ugo Bruzzo{\textquoteright}s 60th birthday 17{\textendash}22 August 2015, Guaruj{\'a}, S{\~a}o Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

}, keywords = {AGT, Donaldson invariants, Equivariant localization, Exact partition function, Supersymmetry, Virasoro conformal blocks}, issn = {0393-0440}, doi = {https://doi.org/10.1016/j.geomphys.2017.01.012}, url = {http://www.sciencedirect.com/science/article/pii/S0393044017300165}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {rossi13085, title = {Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes}, journal = {Proceedings of the National Academy of Sciences}, volume = {114}, number = {50}, year = {2017}, pages = {13085-13090}, abstract = {Active flagella provide the propulsion mechanism for a large variety of swimming eukaryotic microorganisms, from protists to sperm cells. Planar and helical beating patterns of these structures are recurrent and widely studied. The fast spinning motion of the locomotory flagellum of the alga Euglena gracilis constitutes a remarkable exception to these patterns. We report a quantitative description of the 3D flagellar beating in swimming E. gracilis. Given their complexity, these shapes cannot be directly imaged with current microscopy techniques. We show how to overcome these limitations by developing a method to reconstruct in full the 3D kinematics of the cell from conventional 2D microscopy images, based on the exact characterization of the helical motion of the cell body.The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement.}, doi = {10.1073/pnas.1708064114}, url = {https://www.pnas.org/content/114/50/13085}, author = {Massimiliano Rossi and Giancarlo Cicconofri and Alfred Beran and Giovanni Noselli and Antonio DeSimone} } @inbook {ChinestaHuertaRozzaWillcox2017, title = {Model Reduction Methods}, booktitle = {Encyclopedia of Computational Mechanics Second Edition}, year = {2017}, pages = {1-36}, publisher = {John Wiley \& Sons}, organization = {John Wiley \& Sons}, chapter = {Model Reduction Methods}, abstract = {

This chapter presents an overview of model order reduction {\textendash} a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control {\textendash} critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1\&isAllowed=y

}, doi = {10.1002/9781119176817.ecm2110}, author = {Francisco Chinesta and Antonio Huerta and Gianluigi Rozza and Karen Willcox} } @article {20.500.11767_11953, title = {A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {316}, year = {2017}, pages = {522{\textendash}546}, doi = {10.1016/j.cma.2016.08.008}, url = {http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H}, author = {Luca Heltai and Kiendl, J. and Antonio DeSimone and Alessandro Reali} } @article {2017, title = {Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts}, journal = {Biomechanics and Modeling in Mechanobiology}, volume = {16}, year = {2017}, pages = {1373-1399}, doi = {10.1007/s10237-017-0893-7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851\&doi=10.1007\%2fs10237-017-0893-7\&partnerID=40\&md5=c388f20bd5de14187bad9ed7d9affbd0}, author = {F. Ballarin and Elena Faggiano and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Sonia Ippolito and Roberto Scrofani} } @article {2017, title = {POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder}, journal = {Communications in Applied and Industrial Mathematics}, volume = {8}, year = {2017}, pages = {210-236}, abstract = {

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

}, doi = {10.1515/caim-2017-0011}, author = {Giovanni Stabile and Saddam Hijazi and Andrea Mola and Stefano Lorenzi and Gianluigi Rozza} } @article {riccobelli2017rayleigh, title = {Rayleigh{\textendash}Taylor instability in soft elastic layers}, journal = {Phil. Trans. R. Soc. A}, volume = {375}, number = {2093}, year = {2017}, publisher = {The Royal Society}, author = {Davide Riccobelli and Pasquale Ciarletta} } @article {2017, title = {Reduced Basis Methods for Uncertainty Quantification}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, volume = {5}, year = {2017}, month = {08/2017}, pages = {869}, type = {reviewed}, chapter = {813}, abstract = {

In this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babu{\v s}ka, F. Nobile, and R. Tempone,\ SIAM Rev., 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.


Read More:\ http://epubs.siam.org/doi/abs/10.1137/151004550

}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2017, title = {A reduced order model for investigating the dynamics of the Gen-IV LFR coolant pool}, journal = {Applied Mathematical Modelling}, volume = {46}, year = {2017}, pages = {263-284}, doi = {10.1016/j.apm.2017.01.066}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85020006623\&doi=10.1016\%2fj.apm.2017.01.066\&partnerID=40\&md5=f6e5715037eb0ef2ecb9ae03f373294f}, author = {Stefano Lorenzi and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @inbook {BallarinRozzaMaday2017, title = {Reduced-order semi-implicit schemes for fluid-structure interaction problems}, booktitle = {Model Reduction of Parametrized Systems}, year = {2017}, pages = {149{\textendash}167}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, chapter = {Reduced-order semi-implicit schemes for fluid-structure interaction problems}, abstract = {

POD{\textendash}Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

}, doi = {10.1007/978-3-319-58786-8_10}, author = {F. Ballarin and Gianluigi Rozza and Yvon Maday}, editor = {Peter Benner and Mario Ohlberger and Anthony Patera and Gianluigi Rozza and Karsten Urban} } @article {ambrosi2017solid, title = {Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth}, journal = {J. Elast.}, volume = {129}, number = {1-2}, year = {2017}, pages = {107{\textendash}124}, publisher = {Springer Netherlands}, author = {D. Ambrosi and Pezzuto, S. and Davide Riccobelli and Stylianopoulos, T. and Pasquale Ciarletta} } @article {PhysRevLett.119.033901, title = {Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schr{\"o}dinger Equation}, journal = {Phys. Rev. Lett.}, volume = {119}, year = {2017}, month = {Jul}, pages = {033901}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.119.033901}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.033901}, author = {Tikan, Alexey and Billet, Cyril and Gennady El and Alexander Tovbis and Marco Bertola and Sylvestre, Thibaut and Gustave, Francois and Randoux, Stephane and Genty, Go{\"e}ry and Suret, Pierre and Dudley, John M.} } @conference {2016, title = {Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives}, booktitle = {Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering,}, year = {2016}, month = {06/2016}, publisher = {ECCOMAS}, organization = {ECCOMAS}, address = {Crete, Greece}, abstract = {

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

}, author = {Filippo Salmoiraghi and F. Ballarin and Giovanni Corsi and Andrea Mola and Marco Tezzele and Gianluigi Rozza}, editor = {Papadrakakis, M. and Papadopoulos, V. and Stefanou, G. and Plevris, V.} } @article {rizzi2016critical, title = {Critical points of a perturbed Otha-Kawasaki functional}, journal = {arXiv preprint arXiv:1601.07093}, year = {2016}, author = {Matteo Rizzi} } @article {20.500.11767_11949, title = {Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation}, journal = {JOURNAL OF SCIENTIFIC COMPUTING}, volume = {69}, year = {2016}, pages = {430{\textendash}459}, doi = {10.1007/s10915-016-0201-1}, author = {Rotundo, N. and Kim, T. -Y. and Jiang, W. and Luca Heltai and Fried, E.} } @article {Bershtein2016, title = {Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {7}, year = {2016}, month = {Jul}, pages = {23}, abstract = {

We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2016)023}, url = {https://doi.org/10.1007/JHEP07(2016)023}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {2016, title = {A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts}, year = {2016}, institution = {Submitted}, abstract = {A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.}, url = {http://urania.sissa.it/xmlui/handle/1963/35240}, author = {F. Ballarin and Elena Faggiano and Andrea Manzoni and Gianluigi Rozza and Alfio Quarteroni and Sonia Ippolito and Roberto Scrofani and Carlo Antona} } @mastersthesis {2016, title = {Instanton counting on compact manifolds}, year = {2016}, school = {SISSA}, abstract = {In this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. {\textbullet} in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 {\texttimes} S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. {\textbullet} in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2* theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. {\textbullet} in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- stanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web.}, keywords = {Supersymmetry}, url = {http://urania.sissa.it/xmlui/handle/1963/35219}, author = {Massimiliano Ronzani} } @article {2016, title = {Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes}, number = {AMOS Advanced Modelling and Simulation in Engineering Sciences}, year = {2016}, institution = {Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences}, abstract = {In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.}, url = {http://urania.sissa.it/xmlui/handle/1963/35199}, author = {Filippo Salmoiraghi and F. Ballarin and Luca Heltai and Gianluigi Rozza} } @inbook {2016, title = {Model Order Reduction: a survey}, booktitle = {Wiley Encyclopedia of Computational Mechanics, 2016}, year = {2016}, publisher = {Wiley}, organization = {Wiley}, url = {http://urania.sissa.it/xmlui/handle/1963/35194}, author = {Francisco Chinesta and Antonio Huerta and Gianluigi Rozza and Karen Willcox} } @article {11966, title = {A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel}, journal = {Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208}, volume = {87}, number = {Annals of Nuclear Energy;87}, year = {2016}, pages = {208}, publisher = {Elsevier}, chapter = {198}, abstract = {In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.}, doi = {doi:10.1016/j.anucene.2015.09.002}, url = {http://urania.sissa.it/xmlui/handle/1963/35191}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2016, title = {POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations}, year = {2016}, publisher = {Computer Methods in Applied Mechanics and Engineering, Elsevier}, abstract = {Numerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition {\textendash} Reduced Order Model (POD {\textendash} ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.}, author = {Stefano Lorenzi and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {11943, title = {POD{\textendash}Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems}, journal = {International Journal Numerical Methods for Fluids}, year = {2016}, publisher = {Wiley}, abstract = {In this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD){\textendash}Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD{\textendash}Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances}, doi = {10.1002/fld.4252}, author = {F. Ballarin and Gianluigi Rozza} } @mastersthesis {2016, title = {Qualitative properties and construction of solutions to some semilinear elliptic PDEs}, year = {2016}, school = {SISSA}, abstract = {This thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction.}, keywords = {moving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional}, author = {Matteo Rizzi} } @article {11967, title = {A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods}, journal = {NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019}, volume = {2}, number = {Journal of Nuclear Engineering and Radiation Science;2}, year = {2016}, note = {8 pages}, month = {02/2016}, pages = {8}, publisher = {ASME}, abstract = {This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a {\textquotedblleft}classical{\textquotedblright} a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.}, doi = {10.1115/1.4031945}, url = {http://urania.sissa.it/xmlui/handle/1963/35192}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods}, journal = {Communications in Computational Physics}, year = {2016}, month = {2016}, publisher = {SISSA}, abstract = {

In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a {\textquotedblleft}staircase{\textquotedblright} strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as {\textquotedblleft}truth{\textquotedblright} solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine {\textquotedblleft}truth{\textquotedblright} finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34963}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries}, journal = {Computers and Mathematics with Applications }, volume = {71}, year = {2016}, month = {01/2016}, pages = {430}, publisher = {Elsevier}, chapter = {408}, abstract = {The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.}, author = {Laura Iapichino and Alfio Quarteroni and Gianluigi Rozza} } @article {Benvenuti2016, title = {Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {9}, year = {2016}, month = {Sep}, pages = {53}, abstract = {

We explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

}, issn = {1029-8479}, doi = {10.1007/JHEP09(2016)053}, url = {https://doi.org/10.1007/JHEP09(2016)053}, author = {Benvenuti, Sergio and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {farina2016symmetry, title = {Symmetry properties of some solutions to some semilinear elliptic equations}, journal = {Annali della Scuola Normale Superiore di Pisa. Classe di scienze}, volume = {16}, number = {4}, year = {2016}, pages = {1209{\textendash}1234}, publisher = {Classe di Scienze}, author = {Farina, Alberto and Andrea Malchiodi and Matteo Rizzi} } @article {1078-0947_2016_3_1465, title = {Young towers for product systems}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {36}, number = {1078-0947_2016_3_146}, year = {2016}, pages = {1465}, abstract = {

We show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H{\'e}non maps and partially hyperbolic systems.

}, issn = {1078-0947}, doi = {10.3934/dcds.2016.36.1465}, url = {http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642}, author = {Stefano Luzzatto and Marks Ruziboev} } @book {2015, title = {Certified Reduced Basis Methods for Parametrized Partial Differential Equations}, series = {Springer Briefs in Mathematics}, year = {2015}, pages = {135}, publisher = {Springer}, organization = {Springer}, edition = {1}, address = {Switzerland}, abstract = {

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

}, keywords = {a posteriori error bounds, empirical interpolation, parametrized partial differential equations, reduced basis methods, greedy algorithms}, isbn = {978-3-319-22469-5}, issn = {2191-8201}, author = {Jan S Hesthaven and Gianluigi Rozza and Benjamin Stamm} } @article {doi:10.1080/14689367.2015.1046816, title = {Decay of correlations for invertible maps with non-H{\"o}lder observables}, journal = {Dynamical Systems}, volume = {30}, number = {3}, year = {2015}, pages = {341-352}, publisher = {Taylor \& Francis}, abstract = {

An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain H{\'e}non maps and Solenoid maps with intermittency.

}, doi = {10.1080/14689367.2015.1046816}, url = {https://doi.org/10.1080/14689367.2015.1046816}, author = {Marks Ruziboev} } @article {2015, title = {Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization}, year = {2015}, abstract = {In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD{\textendash}Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.}, url = {http://urania.sissa.it/xmlui/handle/1963/34623}, author = {F. Ballarin and Elena Faggiano and Sonia Ippolito and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Roberto Scrofani} } @article {BATTAGLIA2015937, title = {A general existence result for the Toda system on compact surfaces}, journal = {Advances in Mathematics}, volume = {285}, year = {2015}, pages = {937 - 979}, abstract = {

In this paper we consider the following Toda system of equations on a compact surface:-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-Δu1=-4π∑j=1mα1,j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-Δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern{\textendash}Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation-Δu=ρ1(heu∫ΣheudVg-1)-ρ2(he-u∫Σhe-udVg-1), which arises in fluid dynamics."

}, keywords = {Geometric PDEs, Min{\textendash}max schemes, Variational methods}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2015.07.036}, url = {http://www.sciencedirect.com/science/article/pii/S0001870815003072}, author = {Luca Battaglia and Aleks Jevnikar and Andrea Malchiodi and David Ruiz} } @mastersthesis {2015, title = {Gibbs-Markov-Young Structures and Decay of Correlations}, year = {2015}, school = {SISSA}, abstract = {In this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.}, keywords = {Decay of Correlations, GMY-towers}, author = {Marks Ruziboev} } @article {https://doi.org/10.1002/nme.4854, title = {Hourglass stabilization and the virtual element method}, journal = {International Journal for Numerical Methods in Engineering}, volume = {102}, number = {3-4}, year = {2015}, pages = {404-436}, abstract = {SummaryIn this paper, we establish the connections between the virtual element method (VEM) and the hourglass control techniques that have been developed since the early 1980s to stabilize underintegrated C0 Lagrange finite element methods. In the VEM, the bilinear form is decomposed into two parts: a consistent term that reproduces a given polynomial space and a correction term that provides stability. The essential ingredients of -continuous VEMs on polygonal and polyhedral meshes are described, which reveals that the variational approach adopted in the VEM affords a generalized and robust means to stabilize underintegrated finite elements. We focus on the heat conduction (Poisson) equation and present a virtual element approach for the isoparametric four-node quadrilateral and eight-node hexahedral elements. In addition, we show quantitative comparisons of the consistency and stabilization matrices in the VEM with those in the hourglass control method of Belytschko and coworkers. Numerical examples in two and three dimensions are presented for different stabilization parameters, which reveals that the method satisfies the patch test and delivers optimal rates of convergence in the L2 norm and the H1 seminorm for Poisson problems on quadrilateral, hexahedral, and arbitrary polygonal meshes. Copyright {\textcopyright} 2015 John Wiley \& Sons, Ltd.}, keywords = {consistency matrix, hourglass control, polygonal and polyhedral finite elements, stabilization matrix, underintegration, virtual element method}, doi = {https://doi.org/10.1002/nme.4854}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4854}, author = {Andrea Cangiani and Manzini, G. and Russo, A. and Sukumar, N.} } @article {MR3340083, title = {Hourglass stabilization and the virtual element method}, journal = {Internat. J. Numer. Methods Engrg.}, volume = {102}, number = {3-4}, year = {2015}, pages = {404{\textendash}436}, issn = {0029-5981}, doi = {10.1002/nme.4854}, url = {https://doi.org/10.1002/nme.4854}, author = {Andrea Cangiani and Manzini, G. and Russo, A. and Sukumar, N.} } @article {BennerOhlbergerPateraRozzaSorensenUrban2015, title = {Model order reduction of parameterized systems ({MoRePaS}): Preface to the special issue of advances in computational mathematics}, journal = {Advances in Computational Mathematics}, volume = {41}, number = {5}, year = {2015}, pages = {955{\textendash}960}, doi = {10.1007/s10444-015-9443-y}, author = {Peter Benner and Mario Ohlberger and Anthony Patera and Gianluigi Rozza and Sorensen, D.C. and Karsten Urban} } @article {2015, title = {Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations}, journal = {Numerische Mathematik, (2015), 36 p. Article in Press}, number = {Numerische Mathematik;}, year = {2015}, publisher = {Springer}, abstract = {In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.}, doi = {10.1007/s00211-015-0743-4}, url = {http://urania.sissa.it/xmlui/handle/1963/34491}, author = {Gianluigi Rozza and Peng Chen and Alfio Quarteroni} } @article {Bawane2015, title = {N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity}, journal = {Journal of High Energy Physics}, volume = {2015}, number = {7}, year = {2015}, month = {Jul}, pages = {54}, abstract = {

We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2015)054}, url = {https://doi.org/10.1007/JHEP07(2015)054}, author = {Aditya Bawane and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {2015, title = {The phototransduction machinery in the rod outer segment has a strong efficacy gradient}, number = {Proceedings of the National Academy of Sciences of the United States of America;Volume 112, issue 20; pp. E2715-E2724}, year = {2015}, note = {Open Access article}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1423162112}, url = {http://urania.sissa.it/xmlui/handle/1963/35157}, author = {Monica Mazzolini and Giuseppe Facchetti and L. Andolfi and R. Proietti Zaccaria and S. Tuccio and J. Treud and Claudio Altafini and Enzo M. Di Fabrizio and Marco Lazzarino and G. Rapp and Vincent Torre} } @article {2015, title = {Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system}, journal = {Advances in Computational Mathematics}, volume = {special issue for MoRePaS 2012}, year = {2015}, abstract = {

The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

}, keywords = {Domain decomposition, Error estimation, Non-coercive problem, Porous medium equation, Reduced basis method, Stokes flow}, issn = {1019-7168}, doi = { 10.1007/s10444-014-9396-6}, author = {Immanuel Martini and Gianluigi Rozza and Bernard Haasdonk} } @article {PacciariniRozza2015, title = {Reduced basis approximation of parametrized advection-diffusion PDEs with high P{\'e}clet number}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {103}, year = {2015}, pages = {419{\textendash}426}, abstract = {

In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high P{\'e}clet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

}, doi = {10.1007/978-3-319-10705-9__41}, author = {Pacciarini, P. and Gianluigi Rozza} } @article {NegriManzoniRozza2015, title = {Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations}, journal = {Computers and Mathematics with Applications}, volume = {69}, number = {4}, year = {2015}, pages = {319{\textendash}336}, abstract = {

This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

}, doi = {10.1016/j.camwa.2014.12.010}, author = {Federico Negri and Andrea Manzoni and Gianluigi Rozza} } @article {2015, title = {Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations}, number = {International Journal for Numerical Methods in Engineering;Volume 102, issue 5; pp.1136-1161;}, year = {2015}, publisher = {Wiley}, abstract = {In this work, we present a stable proper orthogonal decomposition{\textendash}Galerkin approximation for parametrized steady incompressible Navier{\textendash}Stokes equations with low Reynolds number.}, doi = {10.1002/nme.4772}, url = {http://urania.sissa.it/xmlui/handle/1963/34701}, author = {F. Ballarin and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {Buckling dynamics of a solvent-stimulated stretched elastomeric sheet}, number = {Soft Matter;volume 10; issue 16; pages 2800-2804;}, year = {2014}, publisher = {Royal Society of Chemistry}, abstract = {When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.}, doi = {10.1039/c3sm52941j}, url = {http://urania.sissa.it/xmlui/handle/1963/34967}, author = {Alessandro Lucantonio and Matthieu Roch{\'e} and Paola Nardinocchi and Howard A. Stone} } @article {2014, title = {Comparison between reduced basis and stochastic collocation methods for elliptic problems}, number = {Journal of scientific computing;volume 59; issue 1; pages 187-216;}, year = {2014}, publisher = {Springer}, abstract = {The stochastic collocation method (Babu{\v s}ka et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.}, doi = {10.1007/s10915-013-9764-2}, url = {http://urania.sissa.it/xmlui/handle/1963/34727}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics}, journal = {Annals of Nuclear Energy}, volume = {71}, number = {Annals of Nuclear Energy;volume 71; pages 217-229;}, year = {2014}, month = {09/2014}, pages = {229}, publisher = {Elsevier}, chapter = {217}, abstract = {

In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

}, doi = {10.1016/j.anucene.2014.03.043}, url = {http://urania.sissa.it/xmlui/handle/1963/35039}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Davide Chiesa and Lelio Luzzi and Roberto R. Ponciroli and Ezio Previtali and Marco E. Ricotti and Gianluigi Rozza and Monica Sisti} } @article {2013, title = {On conjugate times of LQ optimal control problems}, number = {Journal of Dynamical and Control Systems}, year = {2014}, note = {14 pages, 1 figure}, publisher = {Springer}, abstract = {Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.}, keywords = {Optimal control, Lagrange Grassmannian, Conjugate point}, doi = {10.1007/s10883-014-9251-6}, url = {http://hdl.handle.net/1963/7227}, author = {Andrei A. Agrachev and Luca Rizzi and Pavel Silveira} } @mastersthesis {2014, title = {The curvature of optimal control problems with applications to sub-Riemannian geometry}, year = {2014}, note = {The PhD thesis is composed of 211 pages and is recorded in PDF format}, school = {SISSA}, abstract = {Optimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp{\textquoteright}s volume and are also investigated.}, keywords = {Sub-Riemannian geometry}, url = {http://hdl.handle.net/1963/7321}, author = {Luca Rizzi} } @article {FortiRozza2014, title = {Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid{\textendash}structure interaction coupling problems}, journal = {International Journal of Computational Fluid Dynamics}, volume = {28}, number = {3-4}, year = {2014}, pages = {158{\textendash}169}, abstract = {We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid{\textendash}structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid{\textendash}structure applications in several fields. The examples provided deal with aeronautics and wind engineering.}, doi = {10.1080/10618562.2014.932352}, author = {Forti, D. and Gianluigi Rozza} } @inbook {2014, title = {Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications}, booktitle = {Separated representations and PGD-based model reduction : fundamentals and applications}, series = { CISM International Centre for Mechanical Sciences}, volume = {554}, year = {2014}, publisher = {Springer}, organization = {Springer}, chapter = {4}, address = {Wien}, abstract = {

In this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

}, keywords = {reduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs}, doi = {10.1007/978-3-7091-1794-1_4}, author = {Gianluigi Rozza} } @article {JaggliIapichinoRozza2014, title = {An improvement on geometrical parameterizations by transfinite maps}, journal = {Comptes Rendus Mathematique}, volume = {352}, number = {3}, year = {2014}, pages = {263{\textendash}268}, abstract = {We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.}, doi = {10.1016/j.crma.2013.12.017}, author = {J{\"a}ggli, C. and Laura Iapichino and Gianluigi Rozza} } @article {2013, title = {A model for crack growth with branching and kinking}, journal = {Asymptotic Analysis}, volume = {89}, year = {2014}, pages = {63-110}, publisher = {SISSA}, type = {Research Article}, chapter = {63}, abstract = {

We study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith{\textquoteright}s theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

}, keywords = {quasistatic crack evolution, branching, kinking, Griffith\\\'s criterion}, doi = {10.3233/ASY-141233}, url = {https://content.iospress.com/articles/asymptotic-analysis/asy1233}, author = {Simone Racca} } @article {2014, title = {Model Order Reduction in Fluid Dynamics: Challenges and Perspectives}, number = {Modeling simulation and applications;volume 9; pages 235-273;}, year = {2014}, publisher = {Springer}, abstract = {This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.}, doi = {10.1007/978-3-319-02090-7_9}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {Rate-independent damage in thermo-viscoelastic materials with inertia}, number = {SISSA;52/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature.}, url = {http://urania.sissa.it/xmlui/handle/1963/7444}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @conference {IapichinoQuarteroniRozzaVolkwein2014, title = {Reduced basis method for the Stokes equations in decomposable domains using greedy optimization}, booktitle = {ECMI 2014 proceedings}, year = {2014}, pages = {1{\textendash}7}, author = {Laura Iapichino and Alfio Quarteroni and Gianluigi Rozza and Volkwein, Stefan} } @book {2014, title = {Reduced Order Methods for Modeling and Computational Reduction}, series = {MS\&A}, volume = {9}, year = {2014}, pages = {334}, publisher = {Springer}, organization = {Springer}, edition = {1}, address = {Milano}, abstract = {

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

}, keywords = {reduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis}, issn = {978-3-319-02089-1}, doi = {10.1007/978-3-319-02090-7}, author = {Alfio Quarteroni and Gianluigi Rozza} } @proceedings {2014, title = {A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics}, number = {International Conference on Nuclear Engineering, Proceedings, ICONE;volume 5;}, year = {2014}, note = {2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131;}, month = {07/2014}, pages = {V005T17A048-V005T17A048}, publisher = {American Society of Mechanical Engineers (ASME)}, edition = {American Society Mechanical Engineering}, address = {Prague, Czech Republic}, abstract = {

In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

}, isbn = {978-079184595-0}, doi = {10.1115/ICONE22-30707}, url = {http://urania.sissa.it/xmlui/handle/1963/35123}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2014, title = {Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows}, number = {Journal of scientific computing;volume 60; issue 3; pages 537-563;}, year = {2014}, publisher = {Springer}, abstract = {Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.}, doi = {10.1007/s10915-013-9807-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34698}, author = {F. Ballarin and Andrea Manzoni and Gianluigi Rozza and Sandro Salsa} } @article {2014, title = {Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics}, number = {SISSA;53/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {This note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data.}, url = {http://urania.sissa.it/xmlui/handle/1963/7463}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @article {PacciariniRozza2014, title = {Stabilized reduced basis method for parametrized advection-diffusion PDEs}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {274}, year = {2014}, pages = {1{\textendash}18}, abstract = {

In this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the {\textquoteleft}{\textquoteleft}double{\textquoteright}{\textquoteright} stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

}, doi = {10.1016/j.cma.2014.02.005}, author = {Pacciarini, P. and Gianluigi Rozza} } @conference {PacciariniRozza2014a, title = {Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher P{\'e}clet number: Roles of the boundary layers and inner fronts}, booktitle = {11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014}, year = {2014}, pages = {5614{\textendash}5624}, abstract = {

Advection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

}, url = {https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf}, author = {Pacciarini, P. and Gianluigi Rozza} } @article {10829, title = {A variational model for the quasi-static growth of fractional dimensional brittle fractures}, number = {Interfaces and Free Boundaries}, year = {2014}, publisher = {European Mathematical Society}, abstract = {

We propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

}, keywords = {Variational models}, doi = {10.4171/IFB/328}, url = {http://hdl.handle.net/1963/6983}, author = {Simone Racca and Rodica Toader} } @article {2014, title = {A weighted empirical interpolation method: A priori convergence analysis and applications}, number = {ESAIM: Mathematical Modelling and Numerical Analysis;volume 48; issue 4; pages 943-953}, year = {2014}, publisher = {EDP Sciences}, abstract = {We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Lo{\`e}ve expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.}, doi = {10.1051/m2an/2013128}, url = {http://urania.sissa.it/xmlui/handle/1963/35021}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {MR2997471, title = {Basic principles of virtual element methods}, journal = {Math. Models Methods Appl. Sci.}, volume = {23}, number = {1}, year = {2013}, pages = {199{\textendash}214}, issn = {0218-2025}, doi = {10.1142/S0218202512500492}, url = {https://doi.org/10.1142/S0218202512500492}, author = {Beir{\~a}o da Veiga, L. and Brezzi, F. and Andrea Cangiani and Manzini, G. and Marini, L. D. and Russo, A.} } @article {2013, title = {A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices}, journal = {Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598}, year = {2013}, publisher = {Elsevier}, abstract = {

We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

}, keywords = {Partial differential equations}, doi = {10.1016/j.crma.2013.07.023}, url = {http://hdl.handle.net/1963/7389}, author = {Denis Devaud and Andrea Manzoni and Gianluigi Rozza} } @article {2013, title = {The curvature: a variational approach}, number = {arXiv:1306.5318;}, year = {2013}, note = {88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group}, institution = {SISSA}, abstract = {The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.}, keywords = {Crurvature, subriemannian metric, optimal control problem}, url = {http://hdl.handle.net/1963/7226}, author = {Andrei A. Agrachev and Davide Barilari and Luca Rizzi} } @article {KoshakjiQuarteroniRozza2013, title = {Free Form Deformation Techniques Applied to 3D Shape Optimization Problems}, journal = {Communications in Applied and Industrial Mathematics}, year = {2013}, abstract = {The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation.}, doi = {10.1685/journal.caim.452}, author = {Anwar Koshakji and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {Monads for framed sheaves on Hirzebruch surfaces}, number = {SISSA preprint;05/2014/mate}, year = {2013}, abstract = {We define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.}, keywords = {Monads, framed sheaves, Hirzebruch surfaces}, author = {Claudio Bartocci and Ugo Bruzzo and Claudio L.S. Rava} } @article {11011, title = {Nonabelian Lie algebroid extensions}, number = {SISSA preprint;06/2014/mate}, year = {2013}, abstract = {

We classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

}, keywords = {Lie algebroids, nonabelian extensions, spectral sequences}, author = {Ugo Bruzzo and Igor Mencattini and Pietro Tortella and Vladimir Rubtsov} } @article {2013, title = {Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants}, journal = {Numerische Mathematik, 2013}, number = {SISSA Preprint;43/2012/M}, year = {2013}, publisher = {Springer}, abstract = {In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.}, keywords = {parametrized Stokes equations}, url = {http://hdl.handle.net/1963/6339}, author = {Gianluigi Rozza and Phuong Huynh and Andrea Manzoni} } @inbook {2015, title = {Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)}, booktitle = {CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches}, volume = {48}, number = {ESAIM Proceedings}, year = {2013}, pages = {98-115}, doi = { http://dx.doi.org/10.1051/proc/201448004}, author = {Denis Devaud and Gianluigi Rozza} } @article {NegriRozzaManzoniQuarteroni2013, title = {Reduced basis method for parametrized elliptic optimal control problems}, journal = {SIAM Journal on Scientific Computing}, volume = {35}, number = {5}, year = {2013}, pages = {A2316{\textendash}A2340}, abstract = {We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique.}, doi = {10.1137/120894737}, author = {Federico Negri and Gianluigi Rozza and Andrea Manzoni and Alfio Quarteroni} } @article {2013, title = {A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics}, number = {SISSA preprint;15/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows}, number = {SISSA preprint;14/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics}, number = {SISSA preprint;13/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Gianluigi Rozza} } @mastersthesis {2013, title = {Some models of crack growth in brittle materials}, year = {2013}, school = {SISSA}, keywords = {Quasi-static crack evolution}, author = {Simone Racca} } @article {ChenQuarteroniRozza2013, title = {Stochastic optimal robin boundary control problems of advection-dominated elliptic equations}, journal = {SIAM Journal on Numerical Analysis}, volume = {51}, number = {5}, year = {2013}, pages = {2700{\textendash}2722}, abstract = {In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided.}, doi = {10.1137/120884158}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {A variational Analysis of the Toda System on Compact Surfaces}, journal = {Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371}, number = {arXiv:1105.3701;}, year = {2013}, note = {pre-peer version, to appear in Comm. Pure Applied Math}, publisher = {Wiley}, abstract = {In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.}, doi = {10.1002/cpa.21433}, url = {http://hdl.handle.net/1963/6558}, author = {Andrea Malchiodi and David Ruiz} } @article {ChenQuarteroniRozza2013a, title = {A weighted reduced basis method for elliptic partial differential equations with random input data}, journal = {SIAM Journal on Numerical Analysis}, volume = {51}, number = {6}, year = {2013}, pages = {3163{\textendash}3185}, abstract = {In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems.}, doi = {10.1137/130905253}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty}, journal = {Mathematical Modelling and Numerical Analysis, in press, 2012-13}, number = {SISSA;42/2012/M}, year = {2012}, publisher = {Cambridge University Press}, abstract = {We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.}, keywords = {shape optimization}, url = {http://hdl.handle.net/1963/6337}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {On a class of vector fields with discontinuity of divide-by-zero type and its applications}, journal = {Journal of dynamical and control systems }, volume = {18}, number = {arXiv:1007.0912;}, year = {2012}, pages = {135-158}, publisher = {Springer}, abstract = {

We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

}, doi = {10.1007/s10883-012-9137-4}, author = {Roberta Ghezzi and Alexey O. Remizov} } @article {2012, title = {Decompositions of large-scale biological systems based on dynamical properties}, journal = {Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83}, number = {PMID:22072388;}, year = {2012}, publisher = {Oxford University Press}, abstract = {MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article.}, doi = {10.1093/bioinformatics/btr620}, url = {http://hdl.handle.net/1963/5226}, author = {Nicola Soranzo and Fahimeh Ramezani and Giovanni Iacono and Claudio Altafini} } @article {2012, title = {Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime}, journal = {Phys. Rev. D 86 (2012) 124035}, number = {arXiv:1206.5315;}, year = {2012}, note = {12 pages, 5 figures}, publisher = {American Physical Society}, abstract = {The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.}, keywords = {Doubly special relativity}, doi = {10.1103/PhysRevD.86.124035}, author = {Giovanni Amelino-Camelia and Antonino Marciano and Marco Matassa and Giacomo Rosati} } @article {2012, title = {A formula for Popp\'s volume in sub-Riemannian geometry}, journal = {Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57}, number = {arXiv:1211.2325;}, year = {2012}, note = {16 pages, minor revisions}, publisher = {SISSA}, abstract = {For an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.}, keywords = {subriemannian, volume, Popp, control}, doi = {10.2478/agms-2012-0004}, url = {http://hdl.handle.net/1963/6501}, author = {Luca Rizzi and Davide Barilari} } @article {2012, title = {Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation}, journal = {Communications in Mathematical Physics 311 (2012) 557-594}, number = {arXiv:1008.2128;}, year = {2012}, publisher = {Springer}, abstract = {We consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy.}, doi = {10.1007/s00220-012-1470-7}, url = {http://hdl.handle.net/1963/6040}, author = {Andrea Raimondo} } @article {2012, title = {A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library}, number = {arXiv:1209.2811;}, year = {2012}, note = {28 pages, 9 figures}, institution = {SISSA}, abstract = {We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.}, keywords = {Finite Element Method, Immersed Boundary Method, Immersed Finite Element Method}, url = {http://hdl.handle.net/1963/6255}, author = {Luca Heltai and Saswati Roy and Francesco Costanzo} } @inbook {2012, title = {Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs}, booktitle = {Springer, Indam Series, Vol. 4, 2012}, number = {SISSA Preprint;44/2012/M}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {The set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.}, keywords = {solution manifold}, url = {http://hdl.handle.net/1963/6340}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {On localization in holomorphic equivariant cohomology}, journal = {Central European Journal of Mathematics, Volume 10, Issue 4, August 2012, Pages 1442-1454}, number = {arXiv:0910.2019;}, year = {2012}, publisher = {Springer}, abstract = {We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu{\textquoteright}s localization formulas.}, keywords = {Lie algebroids}, doi = {10.2478/s11533-012-0054-2}, url = {http://hdl.handle.net/1963/6584}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @proceedings {2012, title = {Reduction strategies for PDE-constrained oprimization problems in Haemodynamics}, number = {SISSA;41/2012/M}, year = {2012}, abstract = {Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.}, keywords = {inverse problems}, url = {http://hdl.handle.net/1963/6338}, author = {Gianluigi Rozza and Andrea Manzoni and Federico Negri} } @article {10671, title = {Simulation-based uncertainty quantification of human arterial network hemodynamics}, journal = {International Journal Numerical Methods Biomedical Engineering}, number = {SISSA preprint;}, year = {2012}, publisher = {Wiley}, abstract = {This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.}, keywords = {uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {A Viscosity-driven crack evolution}, journal = {Advances in Calculus of Variations 5 (2012) 433-483}, number = {SISSA;63/2011/M}, year = {2012}, publisher = {SISSA}, abstract = {

We present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith{\textquoteright}s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

}, doi = {10.1515/acv-2011-0012}, url = {http://hdl.handle.net/1963/5130}, author = {Simone Racca} } @article {ruiz2011, title = {Cluster solutions for the Schr{\"o}dinger-Poisson-Slater problem around a local minimum of the potential}, journal = {Rev. Mat. Iberoamericana}, volume = {27}, number = {1}, year = {2011}, month = {01}, pages = {253{\textendash}271}, publisher = {Real Sociedad Matem{\'a}tica Espa{\~n}ola}, url = {https://projecteuclid.org:443/euclid.rmi/1296828834}, author = {David Ruiz and Giusi Vaira} } @article {2011, title = {New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces}, journal = {Geometric and Functional Analysis 21 (2011) 1196-1217}, number = {SISSA;74/2010/M}, year = {2011}, publisher = {Springer}, abstract = {We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.}, doi = {10.1007/s00039-011-0134-7}, url = {http://hdl.handle.net/1963/4099}, author = {Andrea Malchiodi and David Ruiz} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations in R^n}, journal = {Arch. Rational Mech. Anal. 200 (2011) 1003-1021}, number = {arXiv:1002.4087;}, year = {2011}, publisher = {Springer}, abstract = {

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

}, doi = {10.1007/s00205-010-0381-z}, url = {http://hdl.handle.net/1963/4911}, author = {Stefano Bianchini and Camillo De Lellis and Roger Robyr} } @article {2010, title = {Cohomology of Skew-holomorphic lie algebroids}, number = {SISSA;15/2010/FM}, year = {2010}, abstract = {We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.}, url = {http://hdl.handle.net/1963/3853}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {2010, title = {Existence of planar curves minimizing length and curvature}, journal = {Proc. Steklov Inst. Math. 270 (2010) 43-56}, number = {arXiv.org;0906.5290v2}, year = {2010}, publisher = {Springer}, abstract = {In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.}, doi = {10.1134/S0081543810030041}, url = {http://hdl.handle.net/1963/4107}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Francesco Rossi} } @article {2010, title = {Homogeneous binary trees as ground states of quantum critical Hamiltonians}, journal = {Phys. Rev. A 81 (2010) 062335}, number = {arXiv.org;0912.0466v2}, year = {2010}, publisher = {American Physical Society}, abstract = {

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

}, doi = {10.1103/PhysRevA.81.062335}, url = {http://hdl.handle.net/1963/3909}, author = {Pietro Silvi and Vittorio Giovannetti and Simone Montangero and Matteo Rizzi and J. Ignacio Cirac and Rosario Fazio} } @article {2010, title = {Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems}, journal = {New J. Phys. 12 (2010) 075018}, year = {2010}, publisher = {IOP Publishing}, abstract = {

In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

}, doi = {10.1088/1367-2630/12/7/075018}, url = {http://hdl.handle.net/1963/4067}, author = {Matteo Rizzi and Simone Montangero and Pietro Silvi and Vittorio Giovannetti and Rosario Fazio} } @article {2010, title = {Projective Reeds-Shepp car on $S^2$ with quadratic cost}, journal = {ESAIM COCV 16 (2010) 275-297}, number = {SISSA;34/2008/M}, year = {2010}, abstract = {Fix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.}, doi = {10.1051/cocv:2008075}, url = {http://hdl.handle.net/1963/2668}, author = {Ugo Boscain and Francesco Rossi} } @article {2010, title = {The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures}, journal = {J. Phys. A 43 (2010) 045201}, number = {arXiv.org;0910.1210v1}, year = {2010}, publisher = {IOP Publishing}, abstract = {We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.}, doi = {10.1088/1751-8113/43/4/045201}, url = {http://hdl.handle.net/1963/3846}, author = {Guido Carlet and Paolo Lorenzoni and Andrea Raimondo} } @article {2009, title = {Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity}, journal = {BMC Research Notes (2009) 2:13}, year = {2009}, publisher = {BioMed Central}, abstract = {BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.}, doi = {10.1186/1756-0500-2-13}, url = {http://hdl.handle.net/1963/3706}, author = {Frederic D. Broccard and Silvia Pegoraro and Maria Elisabetta Ruaro and Claudio Altafini and Vincent Torre} } @article {MR2525613, title = {Convergence analysis of the mimetic finite difference method for elliptic problems}, journal = {SIAM J. Numer. Anal.}, volume = {47}, number = {4}, year = {2009}, pages = {2612{\textendash}2637}, issn = {0036-1429}, doi = {10.1137/080717560}, url = {https://doi.org/10.1137/080717560}, author = {Andrea Cangiani and Manzini, Gianmarco and Russo, Alessandro} } @article {2009, title = {Equivariant cohomology and localization for Lie algebroids}, journal = {Funct. Anal. Appl. 43 (2009) 18-29}, number = {SISSA;40/2005/FM}, year = {2009}, abstract = {Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.}, isbn = {978-981-270-377-4}, doi = {10.1007/s10688-009-0003-4}, url = {http://hdl.handle.net/1963/1724}, author = {Ugo Bruzzo and Lucio Cirio and Paolo Rossi and Vladimir Rubtsov} } @article {2009, title = {Gauged Laplacians on quantum Hopf bundles}, journal = {Comm. Math. Phys. 287 (2009) 179-209}, number = {arXiv.org;0801.3376v2}, year = {2009}, publisher = {Springer}, abstract = {We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe {\textquoteleft}excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.}, doi = {10.1007/s00220-008-0672-5}, url = {http://hdl.handle.net/1963/3540}, author = {Giovanni Landi and Cesare Reina and Alessandro Zampini} } @article {2009, title = {Holomorphic equivariant cohomology of Atiyah algebroids and localization}, number = {SISSA;65/2009/FM}, year = {2009}, url = {http://hdl.handle.net/1963/3774}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {2009, title = {The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups}, journal = {J. Funct. Anal. 256 (2009) 2621-2655}, number = {SISSA;33/2008/M}, year = {2009}, abstract = {We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.}, doi = {10.1016/j.jfa.2009.01.006}, url = {http://hdl.handle.net/1963/2669}, author = {Andrei A. Agrachev and Ugo Boscain and Jean-Paul Gauthier and Francesco Rossi} } @article {2008, title = {Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices}, journal = {Phys. Rev. B 77 (2008) 245105}, number = {arXiv.org;0712.3364v1}, year = {2008}, abstract = {

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

}, doi = {10.1103/PhysRevB.77.245105}, url = {http://hdl.handle.net/1963/2694}, author = {Matteo Rizzi and Marco Polini and Miguel A. Cazalilla and M.R. Bakhtiari and Mario P. Tosi and Rosario Fazio} } @article {2008, title = {Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces}, journal = {SIAM J. Control Optim. 47 (2008) 1851-1878}, number = {SISSA;58/2007/M}, year = {2008}, abstract = {In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).}, doi = {10.1137/070703727}, url = {http://hdl.handle.net/1963/2144}, author = {Ugo Boscain and Francesco Rossi} } @article {2008, title = {Multiple bound states for the Schroedinger-Poisson problem}, journal = {Commun. Contemp. Math. 10 (2008) 391-404}, year = {2008}, doi = {10.1142/S021919970800282X}, url = {http://hdl.handle.net/1963/2679}, author = {Antonio Ambrosetti and David Ruiz} } @article {2008, title = {Noncommutative families of instantons}, journal = {Int. Math. Res. Not. vol. 2008, Article ID rnn038}, number = {arXiv.org;0710.0721v2}, year = {2008}, publisher = {Oxford University Press}, abstract = {We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.}, doi = {10.1093/imrn/rnn038}, url = {http://hdl.handle.net/1963/3417}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina and Walter van Suijlekom} } @article {2008, title = {Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn}, journal = {J. Funct. Anal. 254 (2008) 2816-2845}, number = {SISSA;73/2007/M}, year = {2008}, abstract = {Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schr{\"o}dinger equations.}, doi = {10.1016/j.jfa.2007.11.013}, url = {http://hdl.handle.net/1963/2175}, author = {Antonio Ambrosetti and Giovanna Cerami and David Ruiz} } @article {2007, title = {Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas}, journal = {Phys. Rev. Lett. 98 (2007) 030404}, number = {arXiv.org;cond-mat/0609346v1}, year = {2007}, abstract = {

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

}, doi = {10.1103/PhysRevLett.98.030404}, url = {http://hdl.handle.net/1963/2056}, author = {Gao Xianlong and Matteo Rizzi and Marco Polini and Rosario Fazio and Mario P. Tosi and Vivaldo L. Jr. Campo and Klaus Capelle} } @article {2007, title = {Multi-bump solitons to linearly coupled systems of nonlinear Schr{\"o}dinger equations}, number = {SISSA;29/2006/M}, year = {2007}, doi = {10.1007/s00526-006-0079-0}, url = {http://hdl.handle.net/1963/1835}, author = {Antonio Ambrosetti and Eduardo Colorado and David Ruiz} } @article {2007, title = {Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients}, journal = {J. Hyperbolic Differ. Equ. 4 (2007) 771-795}, number = {SISSA;23/2003/M}, year = {2007}, publisher = {World Scientific}, abstract = {We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.}, doi = {10.1142/S0219891607001355}, url = {http://hdl.handle.net/1963/2907}, author = {Giuseppe Maria Coclite and Nils Henrik Risebro} } @article {2006, title = {4e-condensation in a fully frustrated Josephson junction diamond chain}, journal = {Phys. Rev. B 73 (2006) 100502(R)}, number = {arXiv.org;cond-mat/0511423v1}, year = {2006}, abstract = {

Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

}, doi = {10.1103/PhysRevB.73.100502}, url = {http://hdl.handle.net/1963/2400}, author = {Matteo Rizzi and Vittorio Cataudella and Rosario Fazio} } @article {2006, title = {Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity}, journal = {J. Anal. Math. 98 (2006) 317-348}, number = {SISSA;18/2005/M}, year = {2006}, doi = {10.1007/BF02790279}, url = {http://hdl.handle.net/1963/1756}, author = {Antonio Ambrosetti and Andrea Malchiodi and David Ruiz} } @article {2006, title = {A Hopf bundle over a quantum four-sphere from the symplectic group}, journal = {Commun. Math. Phys. 263 (2006) 65-88}, number = {arXiv.org;math/0407342v2}, year = {2006}, abstract = {We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.}, doi = {10.1007/s00220-005-1494-3}, url = {http://hdl.handle.net/1963/2179}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina} } @article {2006, title = {Normal bundles to Laufer rational curves in local Calabi-Yau threefolds}, number = {SISSA;88/2005/FM}, year = {2006}, abstract = {We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.}, doi = {10.1007/s11005-006-0057-7}, url = {http://hdl.handle.net/1963/1785}, author = {Ugo Bruzzo and Antonio Ricco} } @article {2006, title = {Radial solutions concentrating on spheres of nonlinear Schr{\"o}dinger equations with vanishing potentials}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907}, number = {SISSA;38/2005/M}, year = {2006}, abstract = {We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.}, doi = {10.1017/S0308210500004789}, url = {http://hdl.handle.net/1963/1755}, author = {Antonio Ambrosetti and David Ruiz} } @article {2005, title = {Conservation laws with time dependent discontinuous coefficients}, journal = {SIAM J. Math. Anal. 36 (2005) 1293-1309}, number = {SISSA;96/2002/M}, year = {2005}, publisher = {SISSA Library}, abstract = {We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].}, doi = {10.1137/S0036141002420005}, url = {http://hdl.handle.net/1963/1666}, author = {Giuseppe Maria Coclite and Nils Henrik Risebro} } @article {marraEtAl2004, title = {Calculation of impulsively started incompressible viscous flows}, journal = {Int. J. Numer. Meth. Fluids}, volume = {46}, year = {2004}, pages = {877{\textendash}902}, author = {Marra, Andrea and Andrea Mola and Quartapelle, Luigi and Riviello, Luca} } @article {2003, title = {Quantum spin coverings and statistics}, journal = {J. Phys. A 36 (2003), no. 13, 3829-3840}, number = {SISSA;97/2002/FM}, year = {2003}, publisher = {IOP Publishing}, abstract = {SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.}, doi = {10.1088/0305-4470/36/13/314}, url = {http://hdl.handle.net/1963/1667}, author = {Ludwik Dabrowski and Cesare Reina} } @article {2001, title = {A note on the super Krichever map}, journal = {J. Geom. Phys. 37 (2001), no. 1-2, 169-181}, number = {SISSA;36/00/FM}, year = {2001}, publisher = {SISSA Library}, abstract = {We consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa{\textquoteleft}a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian.}, doi = {10.1016/S0393-0440(00)00037-1}, url = {http://hdl.handle.net/1963/1494}, author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa} } @article {2000, title = {3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3}, journal = {Nucl.Phys. B577 (2000) 547-608}, number = {SISSA;113/99/FM}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0550-3213(00)00098-5}, url = {http://hdl.handle.net/1963/1327}, author = {Davide Fabbri and Pietro Fr{\'e} and Leonardo Gualtieri and Cesare Reina and Alessandro Tomasiello and Alberto Zaffaroni and Alessandro Zampa} } @article {2000, title = {A(SLq(2)) at roots of unity is a free module over A(SL(2))}, journal = {Lett. Math. Phys., 2000, 52, 339}, number = {SISSA;42/00/FM}, year = {2000}, publisher = {SISSA Library}, doi = {10.1023/A:1007601131002}, url = {http://hdl.handle.net/1963/1500}, author = {Ludwik Dabrowski and Cesare Reina and Alessandro Zampa} } @article {2000, title = {Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy}, journal = {J. Geom. Phys. 35 (2000), no. 2-3, 239-272}, number = {SISSA;152/99/FM}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0393-0440(00)00007-3}, url = {http://hdl.handle.net/1963/1367}, author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa} } @article {1999, title = {Enhanced gauge symmetries on elliptic K3}, journal = {Phys.Lett. B452 (1999) 244-250}, number = {SISSA;74/98/EP-FM}, year = {1999}, publisher = {Elsevier}, abstract = {We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s.}, doi = {10.1016/S0370-2693(99)00295-6}, url = {http://hdl.handle.net/1963/3366}, author = {Loriano Bonora and Cesare Reina and Alessandro Zampa} } @article {1997, title = {Krichever maps, Fa{\`a} di Bruno polynomials, and cohomology in KP theory}, journal = {Lett. Math. Phys. 42 (1997) 349-361}, number = {SISSA;37/97/FM}, year = {1997}, publisher = {Springer}, abstract = {We study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.}, doi = {10.1023/A:1007323118991}, url = {http://hdl.handle.net/1963/3539}, author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa} } @inbook {1995, title = {Quantum homogeneous spaces at roots of unity}, booktitle = {Quantization, Coherent States and Poisson Structures, Proc. XIVth Workshop on Geometric Methods in Physics, Bialowieza, Poland, 9-15 July 1995, eds. A. Strasburger,\\nS.T. Ali, J.-P. Antoine, J.-P. Gazeau , A. Odzijewicz, Polish Scientific Publisher PWN 1}, number = {SISSA;120/95/FM}, year = {1995}, publisher = {SISSA Library}, organization = {SISSA Library}, url = {http://hdl.handle.net/1963/1022}, author = {Cesare Reina and Alessandro Zampa} } @article {1993, title = {A Borel-Weil-Bott approach to representations of {\rm sl}\sb q(2,C)}, journal = {Lett. Math. Phys. 29 (1993) 215-217}, number = {SISSA;58/93/FM}, year = {1993}, publisher = {Springer}, abstract = {

We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

}, doi = {10.1007/BF00761109}, url = {http://hdl.handle.net/1963/3538}, author = {Davide Franco and Cesare Reina} } @article {1992, title = {Topological "observables" in semiclassical field theories}, journal = {Phys. Lett. B 297 (1992) 82-88}, number = {arXiv.org;hep-th/9209096v1}, year = {1992}, publisher = {Elsevier}, abstract = {

We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}}\ \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

}, doi = {10.1016/0370-2693(92)91073-I}, url = {http://hdl.handle.net/1963/3541}, author = {Margherita Nolasco and Cesare Reina} } @article {1991, title = {On systems of ordinary differential equations with measures as controls}, journal = {Differential Integral Equations 4 (1991), no.4, p.739-765.}, number = {SISSA;82/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/840}, author = {Gianni Dal Maso and Franco Rampazzo} } @article {1990, title = {N=2 super Riemann surfaces and algebraic geometry}, journal = {J. Math. Phys. 31 (1990), no.4, 948-952}, number = {SISSA;47/89/FM}, year = {1990}, publisher = {American Institute of Physics}, abstract = {The geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems.}, doi = {10.1063/1.528775}, url = {http://hdl.handle.net/1963/807}, author = {Cesare Reina and Gregorio Falqui} } @article {1990, title = {A note on the global structure of supermoduli spaces}, journal = {Comm.Math.Phys. 31 (1990), no.4, 948}, number = {SISSA;46/89/FM}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/806}, author = {Cesare Reina and Gregorio Falqui} } @article {1988, title = {On differential systems with vector-valued impulsive controls.}, journal = {Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656}, number = {SISSA;54/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/535}, author = {Alberto Bressan and Franco Rampazzo} } @article {1988, title = {Susy-curves and supermoduli}, number = {SISSA;169/88/FM}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/761}, author = {Gregorio Falqui and Cesare Reina} }