@article {PeschkaHeltai-2022-a, title = {Model hierarchies and higher-order discretisation of time-dependent thin-film free boundary problems with dynamic contact angle}, journal = {Journal of Computational Physics}, volume = {464}, year = {2022}, pages = {111325}, author = {Dirk Peschka and Luca Heltai} } @article {ArndtBangerthFeder-2022-a, title = {The \textttdeal.II Library, Version 9.4}, journal = {Journal of Numerical Mathematics}, year = {2022}, author = {Daniel Arndt and Wolfgang Bangerth Marco Feder and Marc Fehling and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Simon Sticko and Bruno Turcksin and David Wells} } @article {PeschkaZafferiHeltai-2022-a, title = {Variational Approach to Fluid{\textendash}Structure Interaction via GENERIC}, journal = {Journal of Non-Equilibrium Thermodynamics}, year = {2022}, author = {Dirk Peschka and Andrea Zafferi and Luca Heltai and Marita Thomas} } @article {LiuMcBrideSaxena-2022-a, title = {Vibration Analysis of Piezoelectric Kirchhoff-Love shells based on Catmull-Clark Subdivision Surfaces}, journal = {International Journal for Numerical Methods in Engineering}, year = {2022}, author = {Zhaowei Liu and Andrew McBride and Prashant Saxena and Luca Heltai and Yilin Qu and Paul Steinmann} } @article {ArndtBangerthBlais-2021-h, title = {The deal.II Library, Version 9.3}, journal = {Journal of Numerical Mathematics}, year = {2021}, url = {https://doi.org/10.1515/jnma-2021-0081}, author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Marc Fehling and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Uwe K{\"o}cher and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Sebastian Proell and Konrad Simon and Bruno Turcksin and David Wells and Jiaqi Zhang} } @article {HeltaiCaiazzoMueller-2021-a, title = {Multiscale coupling of one-dimensional vascular models and elastic tissues}, journal = {Annals of Biomedical Engineering}, year = {2021}, author = {Luca Heltai and Alfonso Caiazzo and Lucas M{\"u}eller} } @article {HeltaiBangerthKronbichler-2021, title = {Propagating geometry information to finite element computations}, journal = {Transactions on Mathematical Software}, volume = {47}, year = {2021}, pages = {1--30}, chapter = {1}, doi = {https://dx.doi.org/10.1145/3468428}, author = {Luca Heltai and Wolfgang Bangerth and Martin Kronbichler and Andrea Mola} } @article {MulitaGianiHeltai-2021-a, title = {Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods}, journal = {SIAM Journal on Scientific Computing}, year = {2021}, author = {Ornela Mulita and Stefano Giani and Luca Heltai} } @article {GianiGrubisicHeltai-2021-a, title = {Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems}, journal = {Computational Methods in Applied Mathematics}, volume = {21}, number = {2}, year = {2021}, pages = {385-405}, author = {Stefano Giani and Luka Grubisic and Luca Heltai and Ornela Mulita} } @article {ArndtBangerthDavydov-2020-a, title = {The deal.II finite element library: Design, features, and insights}, journal = {Computers and Mathematics with Applications}, year = {2020}, url = {https://doi.org/10.1016/j.camwa.2020.02.022}, author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @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 {AlzettaHeltai-2020-a, title = {Multiscale modeling of fiber reinforced materials via non-matching immersed methods}, journal = {Computers \& Structures}, volume = {239}, year = {2020}, note = {To appear}, pages = {106334}, doi = {10.1016/j.compstruc.2020.106334}, author = {Giovanni Alzetta and Luca Heltai} } @article {Dal-MasoHeltai-2020-a, title = {A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity}, journal = {Journal of Convex Analysis}, year = {2020}, note = {To appear}, url = {https://arxiv.org/abs/2004.12705}, author = {Gianni Dal Maso and Luca Heltai} } @article {HL2020, title = {A priori error estimates of regularized elliptic problems}, journal = {Numerische Mathematik}, volume = {146}, number = {3}, year = {2020}, pages = {571{\textendash}596}, abstract = {Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work we show a-priori rates of convergence of this approximation process in standard Sobolev norms, with minimal regularity assumptions on the approximation of the Dirac delta distribution. The application of these estimates to the numerical solution of elliptic problems with singularly supported forcing terms allows us to provide sharp \$\$H\^1\$\$and \$\$L\^2\$\$error estimates for the corresponding regularized problem. As an application, we show how finite element approximations of a regularized immersed interface method results in the same rates of convergence of its non-regularized counterpart, provided that the support of the Dirac delta approximation is set to a multiple of the mesh size, at a fraction of the implementation complexity. Numerical experiments are provided to support our theories.}, isbn = {0945-3245}, doi = {10.1007/s00211-020-01152-w}, url = {https://doi.org/10.1007/s00211-020-01152-w}, author = {Luca Heltai and Wenyu Lei} } @article {2020, title = {A priori error estimates of regularized elliptic problems}, journal = {Numerische Mathematik}, year = {2020}, author = {Luca Heltai and Wenyu Lei} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Garcia-Sanchez, Daniel and Harper, Graham and Timo Heister and Luca Heltai and Martin Kronbichler and Maguire Kynch, Ross and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, abstract = {This paper provides an overview of the new features of the finite element library deal.II, version 9.1.}, issn = {15702820}, doi = {10.1515/jnma-2019-0064}, author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Garcia-Sanchez, Daniel and Harper, Graham and Timo Heister and Luca Heltai and Martin Kronbichler and Maguire Kynch, Ross and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @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 {HeltaiCaiazzo-2018-a, title = {Multiscale modeling of vascularized tissues via non-matching immersed methods}, journal = {International Journal for Numerical Methods in Biomedical Engineering}, volume = {35}, number = {12}, year = {2019}, pages = {e3264}, url = {https://doi.org/10.1002/cnm.3264}, author = {Luca Heltai and Alfonso Caiazzo} } @article {20.500.11767_81643, title = {Accelerating the iterative solution of convection-diffusion problems using singular value decomposition}, journal = {NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS}, year = {2018}, pages = {1{\textendash}21}, doi = {10.1002/nla.2211}, url = {https://arxiv.org/abs/1807.09467}, author = {Giuseppe Pitton and Luca Heltai} } @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 {20.500.11767_83906, title = {deal2lkit: A toolkit library for high performance programming in deal.II}, journal = {SOFTWAREX}, volume = {7}, year = {2018}, pages = {318{\textendash}327}, doi = {10.1016/j.softx.2018.09.004}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {20.500.11767_81694, title = {The deal.II Library, Version 9.0}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, year = {2018}, doi = {10.1515/jnma-2018-0054}, url = {https://doi.org/10.1515/jnma-2018-0054}, author = {Giovanni Alzetta and Daniel Arndt and Wolfgang Bangerth and Boddu, Vishal and Brands, Benjamin and Denis Davydov and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Kormann, Katharina and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @inbook {20.500.11767_86398, title = {A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids}, booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications}, volume = {16}, year = {2018}, pages = {1{\textendash}21}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-319-96649-6_1}, url = {https://arxiv.org/abs/1712.02545v1}, author = {Boffi, Daniele and Gastaldi, Lucia and Luca Heltai} } @article {20.500.11767_86219, title = {Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments}, journal = {ASTRONOMY \& ASTROPHYSICS}, volume = {618}, year = {2018}, pages = {1{\textendash}14}, doi = {10.1051/0004-6361/201832710}, url = {https://arxiv.org/abs/1801.08937}, author = {Puglisi, Giuseppe and Poletti, Davide and Fabbian, Giulio and Baccigalupi, Carlo and Luca Heltai and Stompor, Radek} } @article {20.500.11767_81737, title = {NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {338}, year = {2018}, pages = {440{\textendash}462}, doi = {10.1016/j.cma.2018.04.039}, url = {https://arxiv.org/abs/1804.08271}, author = {Giuseppe Pitton and Luca Heltai} } @article {20.500.11767_81735, title = {Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions}, journal = {SOFT ROBOTICS}, volume = {5}, year = {2018}, pages = {410{\textendash}424}, doi = {10.1089/soro.2017.0099}, url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/}, author = {Nicola Giuliani and Luca Heltai and Antonio DeSimone} } @article {giulianiEtAl2018, title = {π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods}, journal = {Advances in Engineering Software}, volume = {121}, year = {2018}, pages = {39{\textendash}58}, author = {Nicola Giuliani and Andrea Mola and Luca Heltai} } @article {20.500.11767_47950, title = {The deal.II Library, Version 8.5}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {25}, year = {2017}, pages = {137{\textendash}145}, doi = {10.1515/jnma-2017-0058}, url = {https://www.dealii.org/deal85-preprint.pdf}, author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @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 {MolaHeltaiDeSimone2017, title = {Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations}, journal = {Journal of Ship Research}, volume = {61}, number = {1}, year = {2017}, pages = {1{\textendash}14}, abstract = {

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.

}, doi = {https://doi.org/10.5957/JOSR.61.1.160016}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {20.500.11767_14497, title = {The deal.II Library, Version 8.3}, journal = {ARCHIVE OF NUMERICAL SOFTWARE}, volume = {4}, year = {2016}, pages = {1{\textendash}11}, doi = {10.11588/ans.2016.100.23122}, url = {http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226}, author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin} } @article {20.500.11767_14498, title = {The deal.II library, Version 8.4}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {24}, year = {2016}, pages = {135{\textendash}141}, doi = {10.1515/jnma-2016-1045}, url = {https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf}, author = {Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and David Wells} } @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 {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} } @article {20.500.11767_11950, title = {LinearOperator {\textendash} a generic, high-level expression syntax for linear algebra}, journal = {COMPUTERS \& MATHEMATICS WITH APPLICATIONS}, volume = {72}, year = {2016}, pages = {1{\textendash}24}, doi = {10.1016/j.camwa.2016.04.024}, author = {Matthias Maier and Mauro Bardelloni and Luca Heltai} } @conference {mola2016ship, title = {Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model}, booktitle = {The 26th International Ocean and Polar Engineering Conference}, volume = {3}, year = {2016}, pages = {511{\textendash}518}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {2015, title = {Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems}, journal = {Computers and Mathematics with Applications 69 (2015) 1167{\textendash}1188}, number = {;69}, year = {2015}, abstract = {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.}, doi = {10.1016/j.camwa.2015.03.012}, author = {Roy Saswati and Luca Heltai and Francesco Costanzo} } @article {2015, title = {Deal2lkit: a Toolkit Library for High Performance Programming in deal.II}, year = {2015}, publisher = {SISSA}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35006}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {2015, title = {The deal.II Library, Version 8.2}, journal = {Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8}, year = {2015}, abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.2}, doi = {10.11588/ans.2015.100.18031}, url = {http://urania.sissa.it/xmlui/handle/1963/34464}, author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and T. D. Young} } @article {2015, title = {FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows}, journal = {Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22}, year = {2015}, abstract = {

In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov{\textendash}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.

}, doi = {10.1016/j.enganabound.2015.04.006}, url = {http://urania.sissa.it/xmlui/handle/1963/34466}, author = {Nicola Giuliani and Andrea Mola and Luca Heltai and L. Formaggia} } @article {2015, title = {Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils}, journal = {Comput Methods Appl Mech Eng. 2015;284:1147{\textendash}1180}, number = {;284}, year = {2015}, abstract = {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.}, doi = {10.1016/j.cma.2014.11.037}, author = {Andrea Manzoni and Filippo Salmoiraghi and Luca Heltai} } @proceedings {2014, title = {A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures}, year = {2014}, publisher = {SISSA}, abstract = {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.}, keywords = {ship hydrodynamics}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2012, title = {Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D}, number = {Computer Methods in Applied Mechanics and Engineering}, year = {2014}, publisher = {Elsevier}, abstract = {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.}, keywords = {Isogeometric Analysis}, doi = {10.1016/j.cma.2013.09.017}, url = {http://hdl.handle.net/1963/6326}, author = {Luca Heltai and Marino Arroyo and Antonio DeSimone} } @conference {mola2014ship, title = {Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures}, booktitle = {The 24th International Ocean and Polar Engineering Conference}, volume = {4}, year = {2014}, pages = {815{\textendash}822}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {2013, title = {The deal.II Library, Version 8.1}, number = {arXiv:1312.2266;}, year = {2013}, note = {5 pages}, institution = {SISSA}, abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.0.}, url = {http://hdl.handle.net/1963/7236}, author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and T. D. Young} } @article {2012, title = {A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions}, journal = {Engineering Analysis with Boundary Elements, 37(1):128 {\textendash} 143, 2013.}, number = {SISSA;06/2012/M}, year = {2013}, publisher = {SISSA}, abstract = {

We 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.

}, keywords = {Unsteady ship-wave interaction}, url = {http://hdl.handle.net/1963/5669}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @inbook {9897, title = {Computing optimal strokes for low reynolds number swimmers}, booktitle = {Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors,}, number = {The IMA volumes in mathematics and its applications;155}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {

We 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.

}, keywords = {Numerical analysis.}, isbn = {9781461439967}, doi = {10.1007/978-1-4614-3997-4_13}, url = {http://hdl.handle.net/1963/6445}, author = {Antonio DeSimone and Luca Heltai and Fran{\c c}ois Alouges and Lefebvre-Lepot Aline} } @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} } @article {2012, title = {Reverse engineering the euglenoid movement}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879}, year = {2012}, abstract = {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.}, keywords = {microswimmers}, doi = {10.1073/pnas.1213977109}, url = {http://hdl.handle.net/1963/6444}, author = {Marino Arroyo and Luca Heltai and Daniel Mill{\'a}n and Antonio DeSimone} } @conference {Mola2012, title = {A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves}, booktitle = {17th Int. Conf. Ships Shipp. Res.}, year = {2012}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2012, title = {Variational implementation of immersed finite element methods}, journal = {Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127}, number = {arXiv:1110.2063;}, year = {2012}, note = {42 pages, 5 figures, Revision 1}, publisher = {Elsevier}, abstract = {

Dirac-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.

}, keywords = {Turbulent flow}, doi = {10.1016/j.cma.2012.04.001}, url = {http://hdl.handle.net/1963/6462}, author = {Luca Heltai and Francesco Costanzo} } @article {2011, title = {Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers}, journal = {Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387}, number = {SISSA;33/2009/M}, year = {2011}, publisher = {World Scientific}, abstract = {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.}, keywords = {Optimal swimming}, doi = {10.1142/S0218202511005088}, url = {http://hdl.handle.net/1963/3657}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {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.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @article {2010, title = {The role of membrane viscosity in the dynamics of fluid membranes}, number = {SISSA;55/2010/M}, year = {2010}, abstract = {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.}, url = {http://hdl.handle.net/1963/3930}, author = {Marino Arroyo and Antonio DeSimone and Luca Heltai} } @article {2009, title = {Stratos: a code for 3D free surface flows with floating constraints}, number = {SISSA;41/2009/M}, year = {2009}, abstract = {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......}, url = {http://hdl.handle.net/1963/3701}, author = {Antonio DeSimone and B. Bianchi and Luca Heltai} } @article {2009, title = {Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II}, number = {SISSA;42/2009/M}, year = {2009}, abstract = {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.}, url = {http://hdl.handle.net/1963/3700}, author = {Antonio DeSimone and Luca Heltai and Cataldo Manigrasso} }