Preconditioning nonlocal multi-phase flow
We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen–Cahn variational inequalities. The solver is seen to behave mesh independently and to have only a very mild dependence on the number of phase field variables. In addition...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1826308443633352704 |
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| author | Kay, D Styles, V |
| author_facet | Kay, D Styles, V |
| author_sort | Kay, D |
| collection | OXFORD |
| description | We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen–Cahn variational inequalities. The solver is seen to behave mesh independently and to have only a very mild dependence on the number of phase field variables. In addition we prove convergence, in three GMRES iterations, of the approximation of the two phase problem, regardless of mesh size or interfacial width. Numerical results are presented that illustrate the competitiveness of this approach. |
| first_indexed | 2024-03-07T07:19:35Z |
| format | Journal article |
| id | oxford-uuid:4262cce9-8f96-4819-84f9-8dd235f6364e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:19:35Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:4262cce9-8f96-4819-84f9-8dd235f6364e2022-09-15T13:17:46ZPreconditioning nonlocal multi-phase flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4262cce9-8f96-4819-84f9-8dd235f6364eEnglishSymplectic ElementsElsevier2020Kay, DStyles, VWe propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen–Cahn variational inequalities. The solver is seen to behave mesh independently and to have only a very mild dependence on the number of phase field variables. In addition we prove convergence, in three GMRES iterations, of the approximation of the two phase problem, regardless of mesh size or interfacial width. Numerical results are presented that illustrate the competitiveness of this approach. |
| spellingShingle | Kay, D Styles, V Preconditioning nonlocal multi-phase flow |
| title | Preconditioning nonlocal multi-phase flow |
| title_full | Preconditioning nonlocal multi-phase flow |
| title_fullStr | Preconditioning nonlocal multi-phase flow |
| title_full_unstemmed | Preconditioning nonlocal multi-phase flow |
| title_short | Preconditioning nonlocal multi-phase flow |
| title_sort | preconditioning nonlocal multi phase flow |
| work_keys_str_mv | AT kayd preconditioningnonlocalmultiphaseflow AT stylesv preconditioningnonlocalmultiphaseflow |