A GenEO Domain Decomposition method for Saddle Point problems
We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrall...
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.175/ |
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| author | Nataf, Frédéric Tournier, Pierre-Henri |
| author_facet | Nataf, Frédéric Tournier, Pierre-Henri |
| author_sort | Nataf, Frédéric |
| collection | DOAJ |
| description | We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory (Spillane et al., 2014) to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom. |
| format | Article |
| id | doaj-art-ee419badfea24572aa09d0e73ce28199 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-ee419badfea24572aa09d0e73ce281992025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-03-01351S166768410.5802/crmeca.17510.5802/crmeca.175A GenEO Domain Decomposition method for Saddle Point problemsNataf, Frédéric0https://orcid.org/0000-0003-2813-3481Tournier, Pierre-Henri1Laboratoire J.L. Lions, Sorbonne Université, 4 place Jussieu FranceLaboratoire J.L. Lions, Sorbonne Université, 4 place Jussieu FranceWe introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory (Spillane et al., 2014) to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.175/domain decomposition methodnearly incompressible elasticityhigh performance computingsaddle point problemcoarse spacemultiscale finite elementSchur complement |
| spellingShingle | Nataf, Frédéric Tournier, Pierre-Henri A GenEO Domain Decomposition method for Saddle Point problems Comptes Rendus. Mécanique domain decomposition method nearly incompressible elasticity high performance computing saddle point problem coarse space multiscale finite element Schur complement |
| title | A GenEO Domain Decomposition method for Saddle Point problems |
| title_full | A GenEO Domain Decomposition method for Saddle Point problems |
| title_fullStr | A GenEO Domain Decomposition method for Saddle Point problems |
| title_full_unstemmed | A GenEO Domain Decomposition method for Saddle Point problems |
| title_short | A GenEO Domain Decomposition method for Saddle Point problems |
| title_sort | geneo domain decomposition method for saddle point problems |
| topic | domain decomposition method nearly incompressible elasticity high performance computing saddle point problem coarse space multiscale finite element Schur complement |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.175/ |
| work_keys_str_mv | AT nataffrederic ageneodomaindecompositionmethodforsaddlepointproblems AT tournierpierrehenri ageneodomaindecompositionmethodforsaddlepointproblems AT nataffrederic geneodomaindecompositionmethodforsaddlepointproblems AT tournierpierrehenri geneodomaindecompositionmethodforsaddlepointproblems |