Stopping criteria for iterations in finite element methods
This work extends the results of Arioli [1], [2] on stopping criteria for iterative solution methods for linear finite element problems to the case of nonsymmetric positive-definite problems. We show that the residual measured in the norm induced by the symmetric part of the inverse of the system ma...
| Үндсэн зохиолчид: | , , |
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| Формат: | Journal article |
| Хэл сонгох: | English |
| Хэвлэсэн: |
2005
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| _version_ | 1826302984562147328 |
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| author | Arioli, M Loghin, D Wathen, A |
| author_facet | Arioli, M Loghin, D Wathen, A |
| author_sort | Arioli, M |
| collection | OXFORD |
| description | This work extends the results of Arioli [1], [2] on stopping criteria for iterative solution methods for linear finite element problems to the case of nonsymmetric positive-definite problems. We show that the residual measured in the norm induced by the symmetric part of the inverse of the system matrix is relevant to convergence in a finite element context. We then use Krylov solvers to provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria. © Springer-Verlag 2004. |
| first_indexed | 2024-03-07T05:55:44Z |
| format | Journal article |
| id | oxford-uuid:ea6b6ed3-71e7-4ac4-84d0-4aa7df38882f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:55:44Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:ea6b6ed3-71e7-4ac4-84d0-4aa7df38882f2022-03-27T11:02:13ZStopping criteria for iterations in finite element methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ea6b6ed3-71e7-4ac4-84d0-4aa7df38882fEnglishSymplectic Elements at Oxford2005Arioli, MLoghin, DWathen, AThis work extends the results of Arioli [1], [2] on stopping criteria for iterative solution methods for linear finite element problems to the case of nonsymmetric positive-definite problems. We show that the residual measured in the norm induced by the symmetric part of the inverse of the system matrix is relevant to convergence in a finite element context. We then use Krylov solvers to provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria. © Springer-Verlag 2004. |
| spellingShingle | Arioli, M Loghin, D Wathen, A Stopping criteria for iterations in finite element methods |
| title | Stopping criteria for iterations in finite element methods |
| title_full | Stopping criteria for iterations in finite element methods |
| title_fullStr | Stopping criteria for iterations in finite element methods |
| title_full_unstemmed | Stopping criteria for iterations in finite element methods |
| title_short | Stopping criteria for iterations in finite element methods |
| title_sort | stopping criteria for iterations in finite element methods |
| work_keys_str_mv | AT ariolim stoppingcriteriaforiterationsinfiniteelementmethods AT loghind stoppingcriteriaforiterationsinfiniteelementmethods AT wathena stoppingcriteriaforiterationsinfiniteelementmethods |