Tetrahedral Remeshing in the Context of Large-Scale Numerical Simulation and High Performance Computing

Guillaume Balarac and Francesca Basile and Pierre Bénard and Felipe Bordeu and Jean-Baptiste Chapelier and Luca Cirrottola and Guillaume Caumon and Charles Dapogny and Pascal Frey and Algiane Froehly and Giovanni Ghigliotti and Romain Laraufie and Ghislain Lartigue and Capucine Legentil and Renaud Mercier and Vincent Moureau and Chiara Nardoni and Savinien Pertant and Mustapha Zakari. ( 2022 )
in: MathematicS In Action, 11:1 (129-164)

Abstract

The purpose of this article is to discuss several modern aspects of remeshing, which is the task of modifying an ill-shaped tetrahedral mesh with bad size elements so that it features an appropriate density of high-quality elements. After a brief sketch of classical stakes about meshes and local mesh operations, we notably expose (i) how the local size of the elements of a mesh can be adapted to a user-defined prescription (guided, e.g., by an error estimate attached to a numerical simulation), (ii) how a mesh can be deformed to efficiently track the motion of the underlying domain, (iii) how to construct a mesh of an implicitlydefined domain, and (iv) how remeshing procedures can be conducted in a parallel fashion when large-scale applications are targeted. These ideas are illustrated with several applications involving high-performance computing. In particular, we show how mesh adaptation and parallel remeshing strategies make it possible to achieve a high accuracy in large-scale simulations of complex flows, and how the aforementioned methods for meshing implicitly defined surfaces allow to represent faithfully intricate geophysical interfaces, and to account for the dramatic evolutions of shapes featured by shape optimization processes.

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BibTeX Reference

@article{balarac:hal-03344779,
 abstract = {The purpose of this article is to discuss several modern aspects of remeshing, which is the task of modifying an ill-shaped tetrahedral mesh with bad size elements so that it features an appropriate density of high-quality elements. After a brief sketch of classical stakes about meshes and local mesh operations, we notably expose (i) how the local size of the elements of a mesh can be adapted to a user-defined prescription (guided, e.g., by an error estimate attached to a numerical simulation), (ii) how a mesh can be deformed to efficiently track the motion of the underlying domain, (iii) how to construct a mesh of an implicitlydefined domain, and (iv) how remeshing procedures can be conducted in a parallel fashion when large-scale applications are targeted. These ideas are illustrated with several applications involving high-performance computing. In particular, we show how mesh adaptation and parallel remeshing strategies make it possible to achieve a high accuracy in large-scale simulations of complex flows, and how the aforementioned methods for meshing implicitly defined surfaces allow to represent faithfully intricate geophysical interfaces, and to account for the dramatic evolutions of shapes featured by shape optimization processes.},
 author = {Balarac, Guillaume and Basile, Francesca and B{\'e}nard, Pierre and Bordeu, Felipe and Chapelier, Jean-Baptiste and Cirrottola, Luca and Caumon, Guillaume and Dapogny, Charles and Frey, Pascal and Froehly, Algiane and Ghigliotti, Giovanni and Laraufie, Romain and Lartigue, Ghislain and Legentil, Capucine and Mercier, Renaud and Moureau, Vincent and Nardoni, Chiara and Pertant, Savinien and Zakari, Mustapha},
 doi = {10.5802/msia.22},
 hal_id = {hal-03344779},
 hal_local_reference = {TOP},
 hal_version = {v1},
 journal = {{MathematicS In Action}},
 keywords = {remeshing ; implicit domain meshing ; level-set discretization ; topology optimization ; mesh adaptation ; h-adaptation ; error estimator ; metric ; ``lagrangian'' mesh deformation ; distributed memory parallel remeshing ; hybrid RANS/LES ; LES ; geophysical inverse problem},
 number = {1},
 pages = {129-164},
 pdf = {https://hal.sorbonne-universite.fr/hal-03344779/file/Tetrahedral_remeshing_for_large_scale_simulation_and_HPC_preprint.pdf},
 publisher = {{Soci{\'e}t{\'e} de Math{\'e}matiques Appliqu{\'e}es et Industrielles (SMAI)}},
 title = {{Tetrahedral Remeshing in the Context of Large-Scale Numerical Simulation and High Performance Computing}},
 url = {https://hal.sorbonne-universite.fr/hal-03344779},
 volume = {11},
 year = {2022}
}