Publications

@article{FederCangianiHeltai-2025-a,

title = {R3MG: R-tree based agglomeration of polytopal grids with applications to multilevel methods},

author = {Marco Feder and Andrea Cangiani and Luca Heltai},

url = {https://www.sciencedirect.com/science/article/pii/S0021999125000567},

doi = {https://doi.org/10.1016/j.jcp.2025.113773},

issn = {0021-9991},

year  = {2025},

date = {2025-01-01},

journal = {Journal of Computational Physics},

volume = {526},

pages = {113773},

abstract = {We present a novel approach to perform agglomeration of polygonal and polyhedral grids based on spatial indices. Agglomeration strategies are a key ingredient in polytopal methods for PDEs as they are used to generate (hierarchies of) computational grids from an initial grid. Spatial indices are specialized data structures that significantly accelerate queries involving spatial relationships in arbitrary space dimensions. We show how the construction of the R-tree spatial database of an arbitrary fine grid offers a natural and efficient agglomeration strategy with the following characteristics: i) the process is fully automated, robust, and dimension-independent, ii) it automatically produces a balanced and nested hierarchy of agglomerates, and iii) the shape of the agglomerates is tightly close to the respective axis aligned bounding boxes. Moreover, the R-tree approach provides a full hierarchy of nested agglomerates which permits fast query and allows for efficient geometric multigrid methods to be applied also to those cases where a hierarchy of grids is not present at construction time. We present several examples based on polygonal discontinuous Galerkin methods, confirming the effectiveness of our approach in the context of challenging three-dimensional geometries and the design of geometric multigrid preconditioners.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AfricaArndtBangerth-2024-a,

title = {The deal.II library, Version 9.6},

author = {Pasquale C. Africa and Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Marc Fehling and Rene Gassmöller and Timo Heister and Luca Heltai and Sebastian Kinnewig and Martin Kronbichler and Matthias Maier and Peter Munch and Magdalena Schreter-Fleischhacker and Jan P. Thiele and Bruno Turcksin and David Wells and Vladimir Yushutin},

url = {https://doi.org/10.1515/jnma-2024-0137},

doi = {doi:10.1515/jnma-2024-0137},

year  = {2024},

date = {2024-01-01},

journal = {Journal of Numerical Mathematics},

volume = {32},

number = {4},

pages = {369–380},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PianiFarrellLei-2024-a,

title = {Data-driven solutions of ill-posed inverse problems arising from doping reconstruction in semiconductors},

author = {Stefano Piani and Patricio Farrell and Wenyu Lei and Nella Rotundo and Luca Heltai},

url = {https://doi.org/10.1080/27690911.2024.2323626},

doi = {10.1080/27690911.2024.2323626},

year  = {2024},

date = {2024-01-01},

journal = {Applied Mathematics in Science and Engineering},

volume = {32},

number = {1},

pages = {2323626},

publisher = {Taylor & Francis},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{LeiPianiFarrell-2024-a,

title = {A weighted Hybridizable Discontinuous Galerkin method for drift-diffusion problems},

author = {Wenyu Lei and Stefano Piani and Patricio Farrell and Nella Rotundo and Luca Heltai},

url = {https://dx.doi.org/10.1007/s10915-024-02481-w},

year  = {2024},

date = {2024-01-01},

urldate = {2024-01-01},

journal = {Journal of Scientific Computing},

volume = {99},

number = {33},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiLei-2023-a,

title = {Adaptive Finite Element Approximations for Elliptic Problems using Regularized Forcing Data},

author = {Luca Heltai and Wenyu Lei},

url = {https://doi.org/10.1137/21m1455991},

doi = {10.1137/21m1455991},

year  = {2023},

date = {2023-03-01},

journal = {SIAM Journal on Numerical Analysis},

volume = {61},

number = {2},

pages = {431–456},

publisher = {Society for Industrial & Applied Mathematics (SIAM)},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BoffiCangianiFeder-2023-b,

title = {A comparison of non-matching techniques for the finite element approximation of interface problems},

author = {Daniele Boffi and Andrea Cangiani and Marco Feder and Lucia Gastaldi and Luca Heltai},

url = {https://www.sciencedirect.com/science/article/pii/S0898122123004029},

doi = {https://doi.org/10.1016/j.camwa.2023.09.017},

issn = {0898-1221},

year  = {2023},

date = {2023-01-01},

journal = {Computers & Mathematics with Applications},

volume = {151},

pages = {101-115},

abstract = {We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the implementation aspects and to the analysis of the costs related to the different phases of the simulations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{WichrowskiKrzyzanowskiHeltai-2023-a,

title = {Exploiting high-contrast Stokes preconditioners to efficiently solve incompressible fluid–structure interaction problems},

author = {Michał Wichrowski and Piotr Krzyżanowski and Luca Heltai and Stanisław Stupkiewicz},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7350},

doi = {https://doi.org/10.1002/nme.7350},

year  = {2023},

date = {2023-01-01},

journal = {International Journal for Numerical Methods in Engineering},

volume = {124},

number = {24},

pages = {5446-5470},

abstract = {Abstract In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid–structure interaction problems using a matrix-free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek–Hron benchmarks in two and three dimensions, and investigate timing and scalability results.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{LiuMcBrideGhosh-2023-a,

title = {Computational instability analysis of inflated hyperelastic thin shells using subdivision surfaces},

author = {Zhaowei Liu and Andrew McBride and Abhishek Ghosh and Luca Heltai and Weicheng Huang and Tiantang Yu and Paul Steinmann and Prashant Saxena},

year  = {2023},

date = {2023-01-01},

journal = {Computational Mechanics},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiZunino-2023-a,

title = {Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains},

author = {Luca Heltai and Paolo Zunino},

doi = {10.1142/S0218202523500525},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

journal = {Mathematical Models and Methods in Applied Sciences},

volume = {33},

number = {12},

pages = {2425-2462},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{JoachimDaunaisBibeau-2023-a,

title = {A parallel and adaptative Nitsche immersed boundary method to simulate viscous mixing},

author = {Jeanne Joachim and Carole-Anne Daunais and Valérie Bibeau and Luca Heltai and Bruno Blais},

url = {https://www.sciencedirect.com/science/article/pii/S002199912300284X},

doi = {https://doi.org/10.1016/j.jcp.2023.112189},

issn = {0021-9991},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Computational Physics},

pages = {112189},

abstract = {In this study, we present a parallel immersed boundary strategy that uses Nitsche's method (noted NIB) to weakly impose on a given fluid the boundary conditions associated with a solid of arbitrary shape and motion. Specific details of the software implementation, as done in the software Lethe, are discussed. We verify the NIB method and compare it with other methods in the literature on the well-established test cases of Taylor-Couette flow and von Karman vortex street. Then, we validate the NIB method through simulations of the mixing of fluid in a stirred tank, which is a process central to industries as diverse as polymer manufacturing, food processing, pharmaceutical or chemicals. Simulation results show excellent agreement with experimental data available in the literature for a large range of Reynolds numbers (Image 1), for baffled and unbaffled tanks with a pitched-blade turbine (PBT) impeller. Lastly, the versatility of the NIB method is demonstrated with simulations of a mixing rig with two off-centered impellers with overlapping swept volumes, a case that is either unpractical or impossible to simulate with other largely used techniques. The Software as well as all the files that we used for the simulations are available in the public domain for ease of reproducibility.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{LiuMcBrideSaxena-2022-a,

title = {Vibration Analysis of Piezoelectric Kirchhoff-Love shells based on Catmull-Clark Subdivision Surfaces},

author = {Zhaowei Liu and Andrew McBride and Prashant Saxena and Luca Heltai and Yilin Qu and Paul Steinmann},

url = {https://doi.org/10.1002/nme.7010},

doi = {10.1002/nme.7010},

year  = {2022},

date = {2022-09-01},

journal = {International Journal for Numerical Methods in Engineering},

volume = {123},

number = {18},

pages = {4296-4322},

publisher = {Wiley},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PeschkaHeltai-2022-a,

title = {Model hierarchies and higher-order discretisation of time-dependent thin-film free boundary problems with dynamic contact angle},

author = {Dirk Peschka and Luca Heltai},

url = {https://doi.org/10.1016/j.jcp.2022.111325},

doi = {10.1016/j.jcp.2022.111325},

year  = {2022},

date = {2022-09-01},

journal = {Journal of Computational Physics},

volume = {464},

pages = {111325},

publisher = {Elsevier BV},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArndtBangerthFeder-2022-a,

title = {The deal.II library, Version 9.4},

author = {Daniel Arndt and Wolfgang Bangerth and Marco Feder and Marc Fehling and Rene Gassmöller 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},

url = {https://doi.org/10.1515/jnma-2022-0054},

doi = {10.1515/jnma-2022-0054},

year  = {2022},

date = {2022-07-01},

journal = {Journal of Numerical Mathematics},

volume = {30},

number = {3},

pages = {231–246},

publisher = {Walter de Gruyter GmbH},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PeschkaZafferiHeltai-2022-a,

title = {Variational Approach to Fluid–Structure Interaction via GENERIC},

author = {Dirk Peschka and Andrea Zafferi and Luca Heltai and Marita Thomas},

url = {https://doi.org/10.1515/jnet-2021-0081},

doi = {10.1515/jnet-2021-0081},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Non-Equilibrium Thermodynamics},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiBangerthKronbichler-2021,

title = {Propagating geometry information to finite element computations},

author = {Luca Heltai and Wolfgang Bangerth and Martin Kronbichler and Andrea Mola},

url = {https://dx.doi.org/10.1145/3468428},

year  = {2021},

date = {2021-12-01},

journal = {Transactions on Mathematical Software},

volume = {47},

number = {4},

pages = {1–30},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArndtBangerthBlais-2021-a,

title = {The deal.II library, Version 9.3},

author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Marc Fehling and Rene Gassmöller and Timo Heister and Luca Heltai and Uwe Köcher 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},

url = {https://doi.org/10.1515/jnma-2021-0081},

doi = {10.1515/jnma-2021-0081},

year  = {2021},

date = {2021-09-01},

journal = {Journal of Numerical Mathematics},

volume = {29},

number = {3},

pages = {171–186},

publisher = {Walter de Gruyter GmbH},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiCaiazzoMueller-2021-a,

title = {Multiscale Coupling of One-dimensional Vascular Models and Elastic Tissues},

author = {Luca Heltai and Alfonso Caiazzo and Lucas O. Müller},

url = {https://doi.org/10.1007/s10439-021-02804-0},

doi = {10.1007/s10439-021-02804-0},

year  = {2021},

date = {2021-01-01},

journal = {Annals of Biomedical Engineering},

volume = {49},

pages = {3243–3254},

publisher = {Springer Science and Business Media LLC},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MulitaGianiHeltai-2021-a,

title = {Quasi-Optimal Mesh Sequence Construction through Smoothed Adaptive Finite Element Methods},

author = {Ornela Mulita and Stefano Giani and Luca Heltai},

url = {https://doi.org/10.1137/19m1262097},

doi = {10.1137/19m1262097},

year  = {2021},

date = {2021-01-01},

journal = {SIAM Journal on Scientific Computing},

volume = {43},

number = {3},

pages = {A2211–A2241},

publisher = {Society for Industrial & Applied Mathematics (SIAM)},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{GianiGrubisicHeltai-2021-a,

title = {Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems},

author = {Stefano Giani and Luka Grubisic and Luca Heltai and Ornela Mulita},

url = {https://doi.org/10.1515/cmam-2020-0027},

year  = {2021},

date = {2021-01-01},

journal = {Computational Methods in Applied Mathematics},

volume = {21},

number = {2},

pages = {385-405},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArndtBangerthDavydov-2021-a,

title = {The deal.II finite element library: Design, features, and insights},

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},

url = {https://doi.org/10.1016/j.camwa.2020.02.022},

doi = {10.1016/j.camwa.2020.02.022},

year  = {2021},

date = {2021-01-01},

journal = {Computers & Mathematics with Applications},

volume = {81},

pages = {407–422},

publisher = {Elsevier BV},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Dal-MasoHeltai-2021-a,

title = {A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity},

author = {Gianni Dal Maso and Luca Heltai},

url = {https://arxiv.org/abs/2004.12705},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Convex Analysis},

volume = {28},

number = {2},

pages = {535–548},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AlzettaHeltai-2020-a,

title = {Multiscale modeling of fiber reinforced materials via non-matching immersed methods},

author = {Giovanni Alzetta and Luca Heltai},

url = {https://doi.org/10.1016/j.compstruc.2020.106334},

doi = {10.1016/j.compstruc.2020.106334},

year  = {2020},

date = {2020-10-01},

journal = {Computers & Structures},

volume = {239},

pages = {106334},

publisher = {Elsevier BV},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArndtBangerthBlais-2020-a,

title = {The deal.II library, Version 9.2},

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},

url = {https://doi.org/10.1515/jnma-2020-0043},

doi = {10.1515/jnma-2020-0043},

year  = {2020},

date = {2020-09-01},

journal = {Journal of Numerical Mathematics},

volume = {28},

number = {3},

pages = {131–146},

publisher = {Walter de Gruyter GmbH},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiLei-2020-a,

title = {A priori error estimates of regularized elliptic problems},

author = {Luca Heltai and Wenyu Lei},

url = {https://doi.org/10.1007/s00211-020-01152-w},

year  = {2020},

date = {2020-01-01},

journal = {Numerische Mathematik},

volume = {146},

number = {3},

pages = {571–596},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiRotundo-2019-a,

title = {Error estimates in weighted Sobolev norms for finite element immersed interface methods},

author = {Luca Heltai and Nella Rotundo},

url = {https://doi.org/10.1016/j.camwa.2019.05.029},

doi = {10.1016/j.camwa.2019.05.029},

year  = {2019},

date = {2019-12-01},

journal = {Computers & Mathematics with Applications},

volume = {78},

number = {11},

pages = {3586–3604},

publisher = {Elsevier BV},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArndtBangerthClevenger-2019-a,

title = {The deal.II Library, Version 9.1},

author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Daniel Garcia-Sanchez and Graham Harper and Timo Heister and Luca Heltai and Martin Kronbichler and Ross Maguire Kynch and Matthias Maier and Jean Paul Pelteret and Bruno Turcksin and David Wells},

doi = {10.1515/jnma-2019-0064},

issn = {15702820},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Numerical Mathematics},

abstract = {This paper provides an overview of the new features of the finite element library deal.II, version 9.1.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiCaiazzo-2019-a,

title = {Multiscale modeling of vascularized tissues via nonmatching immersed methods},

author = {Luca Heltai and Alfonso Caiazzo},

url = {https://doi.org/10.1002/cnm.3264},

year  = {2019},

date = {2019-01-01},

journal = {International Journal for Numerical Methods in Biomedical Engineering},

volume = {35},

number = {12},

pages = {e3264},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{GiulianiHeltaiDeSimone-2018-a,

title = {Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions},

author = {Nicola Giuliani and Luca Heltai and Antonio DeSimone},

url = {https://doi.org/10.1089/soro.2017.0099},

doi = {10.1089/soro.2017.0099},

year  = {2018},

date = {2018-08-01},

journal = {Soft Robotics},

volume = {5},

number = {4},

pages = {410–424},

publisher = {Mary Ann Liebert Inc},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PuglisiPolettiFabbian-2018-a,

title = {Iterative map-making with two-level preconditioning for polarized Cosmic Microwave Background data sets},

author = {Giuseppe Puglisi and Davide Poletti and Giulio Fabbian and Carlo Baccigalupi and Luca Heltai and Radek Stompor},

url = {https://doi.org/10.1051/0004-6361/201832710},

year  = {2018},

date = {2018-01-01},

journal = {Astronomy & Astrophysics},

volume = {618},

number = {A62},

abstract = {An estimation of the sky signal from streams of Time Ordered Data (TOD) acquired by Cosmic Microwave Background ($backslash$cmb) experiments is one of the most important steps in the context of $backslash$cmb data analysis referred to as the map-making problem. The continuously growing $backslash$cmb data sets render the $backslash$cmb map-making problem more challenging in terms of computational cost and memory in particular in the context of ground based experiments. In this context, we study a novel class of the Preconditioned Conjugate Gradient (PCG) solvers which invoke two-level preconditioners. We compare them against PCG solvers commonly used in the map-making context considering their precision and time-to-solution. We compare these new methods on realistic, simulated data sets reflecting the characteristics of current and forthcoming $backslash$cmb ground-based experiment. We develop an embarrassingly parallel implementation of the approach where each processor performs a sequential map-making for a subset of the TOD. We find that considering the map level residuals the new class of solvers permits achieving tolerance of up to 3 orders of magnitude better than the standard approach, where the residual level often saturates before convergence is reached. This corresponds to an important improvement in the precision of recovered power spectra in particular on the largest angular scales. The new method also typically requires fewer iterations to reach a required precision and thus shorter runtimes for a single map-making solution. However, the construction of an appropriate two-level preconditioner can be as costly as a single standard map-making run. Nevertheless, if the same problem needs to be solved multiple times, e.g., as in Monte Carlo simulations, this cost has to be incurred only once, and the method should be competitive not only as far as its precision but also its performance is concerned.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{SartoriGiulianiBardelloni-2018-a,

title = {deal2lkit: A toolkit library for high performance programming in deal.II},

author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai},

url = {https://linkinghub.elsevier.com/retrieve/pii/S2352711018302048},

doi = {10.1016/j.softx.2018.09.004},

issn = {23527110},

year  = {2018},

date = {2018-01-01},

journal = {SoftwareX},

volume = {7},

pages = {318–327},

publisher = {Elsevier B.V.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PittonHeltai-2018-b,

title = {Accelerating the iterative solution of convection-diffusion problems using singular value decomposition},

author = {Giuseppe Pitton and Luca Heltai},

year  = {2018},

date = {2018-01-01},

journal = {Numerical Linear Algebra with Applications},

volume = {e2211},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AlzettaArndtBangerth-2018-a,

title = {The deal.II Library, Version 9.0},

author = {Giovanni Alzetta and Daniel Arndt and Wolfgang Bangerth and Vishal Boddu and Benjamin Brands and Denis Davydov and Rene Gassmöller and Timo Heister and Luca Heltai and Katharina Kormann and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells},

url = {https://doi.org/10.1515/jnma-2018-0054},

year  = {2018},

date = {2018-01-01},

journal = {Journal of Numerical Mathematics},

volume = {26},

number = {4},

pages = {173-183},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PittonHeltai-2018-a,

title = {NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces},

author = {Giuseppe Pitton and Luca Heltai},

url = {https://doi.org/10.1016/j.cma.2018.04.039},

year  = {2018},

date = {2018-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

number = {338},

pages = {440–462},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{GiulianiMolaHeltai-2018-a,

title = {π - BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods},

author = {Nicola Giuliani and Andrea Mola and Luca Heltai},

url = {https://doi.org/10.1016/j.advengsoft.2018.03.008},

doi = {10.1016/j.advengsoft.2018.03.008},

issn = {0965-9978},

year  = {2018},

date = {2018-01-01},

journal = {Advances in Engineering Software},

volume = {121},

number = {March},

pages = {39–58},

publisher = {Elsevier},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RafieiNorooziHeltai-2017-a,

title = {An authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production},

author = {Saeedeh Rafiei and Babak Noroozi and Luca Heltai and Akbar Khodaparast Haghi},

url = {https://doi.org/10.1177/1528083717710711},

doi = {10.1177/1528083717710711},

year  = {2017},

date = {2017-05-01},

journal = {Journal of Industrial Textiles},

volume = {47},

number = {7},

pages = {1791–1811},

publisher = {SAGE Publications},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiKiendlDeSimone-2016,

title = {A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling},

author = {Luca Heltai and Josef Kiendl and Antonio DeSimone and Alessandro Reali},

url = {http://dx.doi.org/10.1016/j.cma.2016.08.008},

year  = {2017},

date = {2017-04-01},

journal = {Computer methods in applied mechanics and engineering},

volume = {316},

pages = {522–546},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArndtBangerthDavydov-2017-a,

title = {The textttdeal.II Library, Version 8.5},

author = {D. Arndt and W. Bangerth and D. Davydov and T. Heister and L. Heltai and M. Kronbichler and M. Maier and J. -P. Pelteret and B. Turcksin and D. Wells},

url = {https://doi.org/10.1515/jnma-2017-0058},

year  = {2017},

date = {2017-01-01},

journal = {Journal of Numerical Mathematics},

volume = {25},

number = {3},

pages = {137-145},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MolaHeltaiDeSimone-2017-a,

title = {Wet and Dry Transom Stern Treatment for Fully Nonlinear Potential Flow Simulations of Naval Hydrodynamics},

author = {Andrea Mola and Luca Heltai and Antonio DeSimone},

url = {https://doi.org/10.5957/JOSR.61.1.160016},

year  = {2017},

date = {2017-01-01},

journal = {Journal of Ship Research},

volume = {61},

number = {1},

pages = {1–14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{SalmoiraghiBallarinHeltai-2016-a,

title = {Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes},

author = {Filippo Salmoiraghi and Francesco Ballarin and Luca Heltai and Gianluigi Rozza},

doi = {10.1186/s40323-016-0076-6},

issn = {2213-7467},

year  = {2016},

date = {2016-01-01},

journal = {Advanced Modeling and Simulation in Engineering Sciences},

volume = {3},

number = {1},

pages = {21},

publisher = {Springer International Publishing},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BangerthHeisterHeltai-2016-b,

title = {The deal.II library, Version 8.4},

author = {Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Guido Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and David Wells},

url = {http://dx.doi.org/10.1515/jnma-2016-1045},

doi = {10.1515/jnma-2016-1045},

year  = {2016},

date = {2016-01-01},

journal = {Journal of Numerical Mathematics},

volume = {24},

number = {3},

pages = {135–141},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RotundoKimJiang-2016-a,

title = {Error Analysis of a B-Spline Based Finite-Element Method for Modeling Wind-Driven Ocean Circulation},

author = {Nella Rotundo and Tae-Yeon Kim and Wen Jiang and Luca Heltai and Eliot Fried},

url = {http://dx.doi.org/10.1007/s10915-016-0201-1},

doi = {10.1007/s10915-016-0201-1},

issn = {1573-7691},

year  = {2016},

date = {2016-01-01},

journal = {Journal of Scientific Computing},

volume = {69},

number = {1},

pages = {430–459},

abstract = {We present the results of an error analysis of a B-spline based finite-element approximation of the stream-function formulation of the large scale wind-driven ocean circulation. In particular, we derive optimal error estimates for h-refinement using a Nitsche-type variational formulations of the two simplied linear models of the stationary quasigeostrophic equations, namely the Stommel and Stommel–Munk models. Numerical results obtained from simulations performed on rectangular and embedded geometries confirm the error analysis.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MaierBardelloniHeltai-2016-a,

title = {textttLinearOperator – a generic, high-level expression syntax for linear algebra},

author = {Matthias Maier and Mauro Bardelloni and Luca Heltai},

url = {http://dx.doi.org/10.1016/j.camwa.2016.04.024},

year  = {2016},

date = {2016-01-01},

journal = {Computers and Mathematics with Applications},

volume = {72},

number = {1},

pages = {1-24},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BangerthHeisterHeltai-2016-a,

title = {The deal.II library, Version 8.3},

author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and Guido Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin},

url = {http://journals.ub.uni-heidelberg.de/index.php/ans/article/view/23122},

doi = {10.11588/ans.2016.100.23122},

year  = {2016},

date = {2016-01-01},

journal = {Archive of Numerical Software},

volume = {4},

number = {100},

pages = {1–11},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{GiulianiMolaHeltai-2015-a,

title = {FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows},

author = {Nicola Giuliani and Andrea Mola and Luca Heltai and Luca Formaggia},

year  = {2015},

date = {2015-01-01},

journal = {Engineering Analysis with Boundary Elements},

volume = {59},

pages = {8-22},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{RoyHeltaiCostanzo-2015-a,

title = {Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems},

author = {Saswati Roy and Luca Heltai and Francesco Costanzo},

url = {http://dx.doi.org/10.1016/j.camwa.2015.03.012},

year  = {2015},

date = {2015-01-01},

journal = {Computers and Mathematics with Applications},

volume = {69},

pages = {1167-1188},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BangerthHeisterHeltai-2015-a,

title = {The textttdeal.II Library, Version 8.2},

author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and Guido Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and Toby D. Young},

year  = {2015},

date = {2015-01-01},

journal = {Archive of Numerical Software},

volume = {3},

number = {100},

pages = {1-8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ManzoniSalmoiraghiHeltai-2015-a,

title = {Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils},

author = {Andrea Manzoni and Filippo Salmoiraghi and Luca Heltai},

url = {http://dx.doi.org/10.1016/j.cma.2014.11.037},

year  = {2015},

date = {2015-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {284},

pages = {1147-1180},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiRoyCostanzo-2014-a,

title = {A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library},

author = {Luca Heltai and Saswati Roy and Francesco Costanzo},

url = {http://dx.doi.org/10.11588/ans.2014.1.10946},

year  = {2014},

date = {2014-01-01},

journal = {Archive of Numerical Software},

volume = {2},

number = {1},

pages = {1-27},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiArroyoDeSimone-2013-a,

title = {Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D},

author = {Luca Heltai and Marino Arroyo and Antonio DeSimone},

url = {http://dx.doi.org/10.1016/j.cma.2013.09.017},

year  = {2014},

date = {2014-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {268},

pages = {514-539},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AlougesDeSimoneHeltai-2013-a,

title = {Optimally Swimming Stokesian Robots},

author = {François Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet},

url = {http://dx.doi.org/10.3934/dcdsb.2013.18.1189},

year  = {2013},

date = {2013-01-01},

journal = {Discrete and Continuous Dynamical Systems - Series B},

volume = {18},

number = {5},

pages = {1189-1215},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MolaHeltaiDeSimone-2013-a,

title = {A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions},

author = {Andrea Mola and Luca Heltai and Antonio DeSimone},

url = {http://dx.doi.org/10.1016/j.enganabound.2012.09.005},

year  = {2013},

date = {2013-01-01},

journal = {Engineering Analysis with Boundary Elements},

volume = {37},

number = {1},

pages = {128 - 143},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ArroyoHeltaiMillan-2012-a,

title = {Reverse engineering the euglenoid movement},

author = {Marino Arroyo and Luca Heltai and Daniel Millán and Antonio DeSimone},

url = {http://dx.doi.org/10.1073/pnas.1213977109},

year  = {2012},

date = {2012-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {109},

number = {44},

pages = {17874–17879},

publisher = {David A. Weitz},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HeltaiCostanzo-2012-a,

title = {Variational implementation of immersed finite element methods},

author = {Luca Heltai and Francesco Costanzo},

url = {http://dx.doi.org/10.1016/j.cma.2012.04.001},

year  = {2012},

date = {2012-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {229–232},

number = {0},

pages = {110 - 127},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AlougesDeSimoneHeltai-2011-a,

title = {Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers},

author = {François Alouges and Antonio DeSimone and Luca Heltai},

url = {http://dx.doi.org/10.1142/S0218202511005088},

year  = {2011},

date = {2011-01-01},

journal = {Mathematical Models and Methods in Applied Sciences},

volume = {21},

number = {02},

pages = {361–387},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Heltai-2008-a,

title = {On the stability of the finite element immersed boundary method},

author = {Luca Heltai},

url = {https://doi.org/10.1016/j.compstruc.2007.08.008},

year  = {2008},

date = {2008-01-01},

journal = {Computers & Structures},

volume = {86},

number = {7-8},

pages = {598–617},

abstract = {The immersed boundary (IB) method is a mathematical formulation for fluid-structure interaction problems, where immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid. The original numerical scheme associated to the IB method requires a smoothed approximation of the Dirac delta distribution to link the moving Lagrangian domain with the fixed Eulerian one. We present a stability analysis of the finite element immersed boundary method, where the Dirac delta distribution is treated variationally, in a generalized visco-elastic framework and for two different time-stepping schemes.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BoffiGastaldiHeltai-2008-a,

title = {On the hyper-elastic formulation of the immersed boundary method},

author = {Daniele Boffi and Lucia Gastaldi and Luca Heltai and Charles S. Peskin},

url = {https://doi.org/10.1016/j.cma.2007.09.015},

year  = {2008},

date = {2008-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {197},

number = {25-28},

pages = {2210–2231},

abstract = {The immersed boundary (IB) method is both a mathematical formulation and a numerical method for fluid-structure interaction problems, in which immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid. Previous formulations of the IB method were not able to treat appropriately immersed materials of finite, nonzero thickness modeled by general hyper-elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid-fluid interface. (Such a jump does not arise when the solid is comprised of fibers that run parallel to the interface, but typically does arise in other cases, e.g., when the solid contains elastic fibers that terminate at the solid-fluid interface). We present a derivation of the IB method that takes into account in an appropriate way the missing term. The derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work. The stress is divided into its fluid-like and solid-like components, and each of these two terms is treated in its natural framework, i.e., the Eulerian framework for the fluid-like stress and the Lagrangian framework for the solid-like stress. We describe how the IB method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AntoniettiHeltai-2007-a,

title = {Numerical Validation of a Class of Mixed Discontinuous Galerkin Methods for Darcy Flow},

author = {Paola F. Antonietti and Luca Heltai},

url = {http://dx.doi.org/10.1016/j.cma.2007.05.018},

year  = {2007},

date = {2007-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {196},

number = {45-48},

pages = {4505-4520},

abstract = {We present a thorough set of numerical experiments to confirm the robustness of several 

Discontinuous Galerkin methods proposed for the approximation of Darcy law. 

We perform two- and three-dimensional tests involving both low and high order 

approximations on Cartesian grids and on triangular grids. The tests we present 

confirm the theoretical estimates for symmetric approximations and characterize 

the behavior of non symmetric approximations, where convergence rates that are 

one order better than predicted are observed for suitable choices of approximation 

spaces. Robustness and accuracy of all these methods are assessed for realistic 

numerical experiments where discontinuous permeability coefficients and bounded 

smooth permeability functions are used.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BoffiGastaldiHeltai-2007-a,

title = {On the CFL condition for the finite element immersed boundary method},

author = {Daniele Boffi and Lucia Gastaldi and Luca Heltai},

url = {http://dx.doi.org/10.1016/j.compstruc.2007.01.009},

year  = {2007},

date = {2007-01-01},

journal = {Computers & Structures},

volume = {85},

number = {11-14},

pages = {775–783},

abstract = {The finite element version of the immersed boundary method proved to be a robust alternative to the original one which was based on finite differences. In this paper we highlight the advantages of the new method and discuss a stability analysis for its space-time discretization. Numerical experiments confirm the theoretical results.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BoffiGastaldiHeltai-2007-b,

title = {Numerical stability of the finite element immersed boundary method},

author = {Daniele Boffi and Lucia Gastaldi and Luca Heltai},

url = {http://dx.doi.org/10.1142/S0218202507002352},

year  = {2007},

date = {2007-01-01},

journal = {Mathematical Models and Methods in Applied Sciences},

volume = {17},

number = {10},

pages = {1479-1505},

abstract = {The immersed boundary method is both a 

 mathematical formulation and a numerical method. In 

 its continuous version it is a fully non-linearly 

 coupled formulation for the study of fluid structure 

 interactions. As it is common in these cases, many 

 numerical methods have been introduced to reduce the 

 difficulties related to the non-linear coupling 

 between the structure and the fluid evolution, 

 however numerical instabilities arise when explicit 

 or semi-implicit methods are considered. In this 

 work we present a stability analysis based on energy 

 estimates of the variational formulation of the 

 immersed boundary method. A two dimensional 

 incompressible fluid and a boundary in the form of a 

 simple closed curve are considered. We use a 

 linearization of the Navier-Stokes equations and a 

 linear elasticity model to prove the unconditional 

 stability of the fully implicit discretization, 

 achieved with the use of a backward Euler method for 

 both the fluid and the structure evolution, and a 

 CFL condition for the semi-implicit method where the 

 fluid terms are treated implicitly while the 

 structure is treated explicitly. We present some 

 numerical tests that show good accordance between 

 the observed stability behavior and the one 

 predicted by our results.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}