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 implicitly-defined 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.
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

@article{MSIA_2022__11_1_129_0, author = {G. Balarac and F. Basile and P. B\'enard and F. Bordeu and J.-B. Chapelier and L. Cirrottola and G. Caumon and C. Dapogny and P. Frey and A. Froehly and G. Ghigliotti and R. Laraufie and G. Lartigue and C. Legentil and R. Mercier and V. Moureau and C. Nardoni and S. Pertant and M. Zakari}, title = {Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing}, journal = {MathematicS In Action}, pages = {129--164}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {11}, number = {1}, year = {2022}, doi = {10.5802/msia.22}, language = {en}, url = {https://msia.centre-mersenne.org/articles/10.5802/msia.22/} }
TY - JOUR AU - G. Balarac AU - F. Basile AU - P. Bénard AU - F. Bordeu AU - J.-B. Chapelier AU - L. Cirrottola AU - G. Caumon AU - C. Dapogny AU - P. Frey AU - A. Froehly AU - G. Ghigliotti AU - R. Laraufie AU - G. Lartigue AU - C. Legentil AU - R. Mercier AU - V. Moureau AU - C. Nardoni AU - S. Pertant AU - M. Zakari TI - Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing JO - MathematicS In Action PY - 2022 SP - 129 EP - 164 VL - 11 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - https://msia.centre-mersenne.org/articles/10.5802/msia.22/ DO - 10.5802/msia.22 LA - en ID - MSIA_2022__11_1_129_0 ER -
%0 Journal Article %A G. Balarac %A F. Basile %A P. Bénard %A F. Bordeu %A J.-B. Chapelier %A L. Cirrottola %A G. Caumon %A C. Dapogny %A P. Frey %A A. Froehly %A G. Ghigliotti %A R. Laraufie %A G. Lartigue %A C. Legentil %A R. Mercier %A V. Moureau %A C. Nardoni %A S. Pertant %A M. Zakari %T Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing %J MathematicS In Action %D 2022 %P 129-164 %V 11 %N 1 %I Société de Mathématiques Appliquées et Industrielles %U https://msia.centre-mersenne.org/articles/10.5802/msia.22/ %R 10.5802/msia.22 %G en %F MSIA_2022__11_1_129_0
G. Balarac; F. Basile; P. Bénard; F. Bordeu; J.-B. Chapelier; L. Cirrottola; G. Caumon; C. Dapogny; P. Frey; A. Froehly; G. Ghigliotti; R. Laraufie; G. Lartigue; C. Legentil; R. Mercier; V. Moureau; C. Nardoni; S. Pertant; M. Zakari. Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing. MathematicS In Action, Volume 11 (2022) no. 1, pp. 129-164. doi : 10.5802/msia.22. https://msia.centre-mersenne.org/articles/10.5802/msia.22/
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