Analysis of preconditioners for saddle-point problems
Mixed finite element formulations give rise to large, sparse, block linear systems of equations, the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the fo...
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1797087817331900416 |
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| author | Loghin, D Wathen, A |
| author_facet | Loghin, D Wathen, A |
| author_sort | Loghin, D |
| collection | OXFORD |
| description | Mixed finite element formulations give rise to large, sparse, block linear systems of equations, the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the formulation of the finite element method (the Babuška-Brezzi, or inf-sup, conditions). The analysis is motivated by the notions of norm-equivalence and field-of-values-equivalence of matrices. In particular, we give sufficient conditions for diagonal and triangular block-preconditioners to be norm- and field-of-values-equivalent to the system matrix. |
| first_indexed | 2024-03-07T02:41:04Z |
| format | Journal article |
| id | oxford-uuid:aa799608-7791-4b51-89d8-8fbe3b1505f9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:41:04Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:aa799608-7791-4b51-89d8-8fbe3b1505f92022-03-27T03:15:17ZAnalysis of preconditioners for saddle-point problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:aa799608-7791-4b51-89d8-8fbe3b1505f9EnglishSymplectic Elements at Oxford2004Loghin, DWathen, AMixed finite element formulations give rise to large, sparse, block linear systems of equations, the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the formulation of the finite element method (the Babuška-Brezzi, or inf-sup, conditions). The analysis is motivated by the notions of norm-equivalence and field-of-values-equivalence of matrices. In particular, we give sufficient conditions for diagonal and triangular block-preconditioners to be norm- and field-of-values-equivalent to the system matrix. |
| spellingShingle | Loghin, D Wathen, A Analysis of preconditioners for saddle-point problems |
| title | Analysis of preconditioners for saddle-point problems |
| title_full | Analysis of preconditioners for saddle-point problems |
| title_fullStr | Analysis of preconditioners for saddle-point problems |
| title_full_unstemmed | Analysis of preconditioners for saddle-point problems |
| title_short | Analysis of preconditioners for saddle-point problems |
| title_sort | analysis of preconditioners for saddle point problems |
| work_keys_str_mv | AT loghind analysisofpreconditionersforsaddlepointproblems AT wathena analysisofpreconditionersforsaddlepointproblems |