We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

%B Journal of Ship Research %V 61 %P 1–14 %G eng %R https://doi.org/10.5957/JOSR.61.1.160016 %0 Journal Article %J ARCHIVE OF NUMERICAL SOFTWARE %D 2016 %T The deal.II Library, Version 8.3 %A W. Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %B ARCHIVE OF NUMERICAL SOFTWARE %V 4 %P 1–11 %G eng %U http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226 %R 10.11588/ans.2016.100.23122 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2016 %T The deal.II library, Version 8.4 %A W. Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 24 %P 135–141 %G eng %U https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf %R 10.1515/jnma-2016-1045 %0 Journal Article %J JOURNAL OF SCIENTIFIC COMPUTING %D 2016 %T Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation %A Rotundo, N. %A Kim, T. -Y. %A Jiang, W. %A Luca Heltai %A Fried, E. %B JOURNAL OF SCIENTIFIC COMPUTING %V 69 %P 430–459 %G eng %R 10.1007/s10915-016-0201-1 %0 Report %D 2016 %T Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes %A Filippo Salmoiraghi %A Francesco Ballarin %A Luca Heltai %A Gianluigi Rozza %X 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. %I Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35199 %1 35493 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-06-20T23:55:25Z No. of bitstreams: 1 MAIN_IGA_FFD_ROM.pdf: 1631282 bytes, checksum: b050e472f11943b95d8307915a50b6da (MD5) %0 Journal Article %J COMPUTERS & MATHEMATICS WITH APPLICATIONS %D 2016 %T LinearOperator – a generic, high-level expression syntax for linear algebra %A Matthias Maier %A Mauro Bardelloni %A Luca Heltai %B COMPUTERS & MATHEMATICS WITH APPLICATIONS %V 72 %P 1–24 %G eng %R 10.1016/j.camwa.2016.04.024 %0 Conference Paper %B The 26th International Ocean and Polar Engineering Conference %D 2016 %T Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 26th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 3 %P 511–518 %G eng %0 Journal Article %J Computers and Mathematics with Applications 69 (2015) 1167–1188 %D 2015 %T Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems %A Roy Saswati %A Luca Heltai %A Francesco Costanzo %X We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks. %B Computers and Mathematics with Applications 69 (2015) 1167–1188 %G en %1 34633 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:26:58Z No. of bitstreams: 1 rhc_feibm_validation-v3.pdf: 7039131 bytes, checksum: 705f28e17037504f00766fc4e84a10a4 (MD5) %R 10.1016/j.camwa.2015.03.012 %0 Journal Article %D 2015 %T Deal2lkit: a Toolkit Library for High Performance Programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %X We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35006 %1 35235 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by asartori@sissa.it (asartori@sissa.it) on 2015-11-13T13:12:29Z No. of bitstreams: 1 paper_deal2lkit.pdf: 1085486 bytes, checksum: 1dc7e9b9790fe38d2ced7b5328633cd8 (MD5) %0 Journal Article %J Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %D 2015 %T The deal.II Library, Version 8.2 %A W. Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.2 %B Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %G en %U http://urania.sissa.it/xmlui/handle/1963/34464 %1 34637 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:40:46Z No. of bitstreams: 1 18031-44567-1-PB (1).pdf: 137014 bytes, checksum: 9a5fddeccfa389c32ca89a466e653074 (MD5) %R 10.11588/ans.2015.100.18031 %0 Journal Article %J Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %D 2015 %T FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows %A Nicola Giuliani %A Andrea Mola %A Luca Heltai %A L. Formaggia %XIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

%B Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34466 %1 34640 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by ngiuliani@sissa.it (ngiuliani@sissa.it) on 2015-05-04T12:32:04Z No. of bitstreams: 1 paper-free-surface.pdf: 888763 bytes, checksum: 68366266786e84b78a356acd6de50840 (MD5) %R 10.1016/j.enganabound.2015.04.006 %0 Journal Article %J Comput Methods Appl Mech Eng. 2015;284:1147–1180 %D 2015 %T Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils %A Andrea Manzoni %A Filippo Salmoiraghi %A Luca Heltai %X We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement. %B Comput Methods Appl Mech Eng. 2015;284:1147–1180 %G en %1 34587 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-03-03T16:15:31Z No. of bitstreams: 1 RB_IGA_BEM.pdf: 725470 bytes, checksum: e2fe6fabfdbe6118e9ef07fb185113af (MD5) %R 10.1016/j.cma.2014.11.037 %0 Conference Proceedings %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %D 2014 %T A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K ship hydrodynamics %X We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed. %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %I SISSA %G en %1 7357 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2014-03-22T15:00:37Z No. of bitstreams: 1 MolaHeltaiDeSimone2014.pdf: 1241007 bytes, checksum: 1a56d909a08f1f470c7efc14018e37f8 (MD5) %0 Journal Article %D 2014 %T Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D %A Luca Heltai %A Marino Arroyo %A Antonio DeSimone %K Isogeometric Analysis %X Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM. %I Elsevier %G en %U http://hdl.handle.net/1963/6326 %1 6250 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-12-03T08:19:28Z No. of bitstreams: 1 isogeo_stokes.pdf: 732320 bytes, checksum: 224ef57de6c49f03db0afaccdcb234f9 (MD5) %R 10.1016/j.cma.2013.09.017 %0 Conference Paper %B The 24th International Ocean and Polar Engineering Conference %D 2014 %T Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 24th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 4 %P 815–822 %G eng %0 Report %D 2013 %T The deal.II Library, Version 8.1 %A W. Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.0. %I SISSA %G en %U http://hdl.handle.net/1963/7236 %1 7272 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-12-10T10:43:08Z No. of bitstreams: 1 1312.2266v1.pdf: 245445 bytes, checksum: e00fcd6d7d9ac6e2076208958b07eef3 (MD5) %0 Journal Article %J Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %D 2013 %T A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K Unsteady ship-wave interaction %XWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

%B Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %I SISSA %G en %U http://hdl.handle.net/1963/5669 %1 5457 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-16T11:19:51Z\\nNo. of bitstreams: 1\\nMolaHeltaiDeSimone-2012-aa.pdf: 1981527 bytes, checksum: 8a82da009242da0cf884e2c7f04009a6 (MD5) %0 Book Section %B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %D 2012 %T Computing optimal strokes for low reynolds number swimmers %A Antonio DeSimone %A Luca Heltai %A François Alouges %A Lefebvre-Lepot Aline %K Numerical analysis. %XWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

%B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %I Springer %@ 9781461439967 %G en %U http://hdl.handle.net/1963/6445 %1 6381 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:33:50Z\\nNo. of bitstreams: 0 %R 10.1007/978-1-4614-3997-4_13 %0 Report %D 2012 %T A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library %A Luca Heltai %A Saswati Roy %A Francesco Costanzo %K Finite Element Method %K Immersed Boundary Method %K Immersed Finite Element Method %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/6255 %1 6172 %2 Mathematics %3 Functional Analysis and Applications %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-09-28T11:06:13Z\\nNo. of bitstreams: 1\\n1209.2811v1.pdf: 4766431 bytes, checksum: a46803f7f8daf3195359f65c9161b944 (MD5) %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %D 2012 %T Reverse engineering the euglenoid movement %A Marino Arroyo %A Luca Heltai %A Daniel Millán %A Antonio DeSimone %K microswimmers %X Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. %B Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %G en %U http://hdl.handle.net/1963/6444 %1 6380 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:29:31Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1213977109 %0 Conference Paper %B 17th Int. Conf. Ships Shipp. Res. %D 2012 %T A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %B 17th Int. Conf. Ships Shipp. Res. %G eng %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %D 2012 %T Variational implementation of immersed finite element methods %A Luca Heltai %A Francesco Costanzo %K Turbulent flow %XDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

%B Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %I Elsevier %G en %U http://hdl.handle.net/1963/6462 %1 6389 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2013-02-04T16:21:56Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2012.04.001 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %D 2011 %T Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers %A François Alouges %A Antonio DeSimone %A Luca Heltai %K Optimal swimming %X We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. %B Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3657 %1 648 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-23T17:30:51Z\\r\\nNo. of bitstreams: 1\\r\\nSissa33_2009M.pdf: 708341 bytes, checksum: 6134bd52f083488620fb5bb24bcf9b93 (MD5) %R 10.1142/S0218202511005088 %0 Report %D 2010 %T Optimally swimming Stokesian Robots %A François Alouges %A Antonio DeSimone %A Luca Heltai %A Aline Lefebvre %A Benoit Merlet %X We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail. %G en_US %U http://hdl.handle.net/1963/3929 %1 472 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:02:56Z\\nNo. of bitstreams: 1\\nHeltai_54M_2010.pdf: 993075 bytes, checksum: 77225380bab031438ac940e694ea0e6c (MD5) %0 Report %D 2010 %T The role of membrane viscosity in the dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %A Luca Heltai %X Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. %G en_US %U http://hdl.handle.net/1963/3930 %1 471 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:13:35Z\\nNo. of bitstreams: 1\\nArroyo_55M.pdf: 4419667 bytes, checksum: ca8a9c175a457ad33996d46a08e85e44 (MD5) %0 Report %D 2009 %T Stratos: a code for 3D free surface flows with floating constraints %A Antonio DeSimone %A B. Bianchi %A Luca Heltai %X This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... %G en_US %U http://hdl.handle.net/1963/3701 %1 604 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:37:01Z\\nNo. of bitstreams: 1\\nBianchiDeSimoneHeltai.pdf: 899803 bytes, checksum: aff44eb1a39c6fd4acd4b3cb285e2d64 (MD5) %0 Report %D 2009 %T Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II %A Antonio DeSimone %A Luca Heltai %A Cataldo Manigrasso %X The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. %G en_US %U http://hdl.handle.net/1963/3700 %1 605 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:20:01Z\\nNo. of bitstreams: 1\\nDeSimoneHeltaiManigrasso.pdf: 915137 bytes, checksum: c3144348b6aab67a5f547060049c7847 (MD5)