Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems
We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, ded...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3165 |
| _version_ | 1797502643753451520 |
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| author | Camille Negrello Pierre Gosselet Christian Rey |
| author_facet | Camille Negrello Pierre Gosselet Christian Rey |
| author_sort | Camille Negrello |
| collection | DOAJ |
| description | We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed formulations with dual approach, i.e., nonlinear analogues to the Finite Element Tearing and Interconnecting (FETI) solver. By increasing the importance of local nonlinear operations, this new technique reduces communications between processors throughout the parallel solving process. Moreover, the tangent systems produced at each step still have the exact shape of classically preconditioned linear FETI problems, which makes the tractability of the implementation barely modified. The efficiency of this new preconditioner is illustrated on two academic test cases, namely a water diffusion problem and a nonlinear thermal behavior. |
| first_indexed | 2024-03-10T03:38:02Z |
| format | Article |
| id | doaj.art-57fecf414f0149a48025af714014bda3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:38:02Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-57fecf414f0149a48025af714014bda32023-11-23T09:25:06ZengMDPI AGMathematics2227-73902021-12-01924316510.3390/math9243165Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear ProblemsCamille Negrello0Pierre Gosselet1Christian Rey2ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, FranceENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, FranceSafran Corporate Reseach Center, 92230 Gennevilliers, FranceWe consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed formulations with dual approach, i.e., nonlinear analogues to the Finite Element Tearing and Interconnecting (FETI) solver. By increasing the importance of local nonlinear operations, this new technique reduces communications between processors throughout the parallel solving process. Moreover, the tangent systems produced at each step still have the exact shape of classically preconditioned linear FETI problems, which makes the tractability of the implementation barely modified. The efficiency of this new preconditioner is illustrated on two academic test cases, namely a water diffusion problem and a nonlinear thermal behavior.https://www.mdpi.com/2227-7390/9/24/3165domain decompositionnonlinear problemsNewton solverFETI solverparallel processing |
| spellingShingle | Camille Negrello Pierre Gosselet Christian Rey Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems Mathematics domain decomposition nonlinear problems Newton solver FETI solver parallel processing |
| title | Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems |
| title_full | Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems |
| title_fullStr | Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems |
| title_full_unstemmed | Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems |
| title_short | Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems |
| title_sort | nonlinearly preconditioned feti solver for substructured formulations of nonlinear problems |
| topic | domain decomposition nonlinear problems Newton solver FETI solver parallel processing |
| url | https://www.mdpi.com/2227-7390/9/24/3165 |
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