@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 {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} } @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} } @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 {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} } @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} }