PCPATCH: software for the topological construction of multigrid relaxation methods
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we pr...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Association for Computing Machinery
2021
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| _version_ | 1826263975497564160 |
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| author | Farrell, PE Knepley, MG Mitchell, L Wechsung, F |
| author_facet | Farrell, PE Knepley, MG Mitchell, L Wechsung, F |
| author_sort | Farrell, PE |
| collection | OXFORD |
| description | Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems. |
| first_indexed | 2024-03-06T20:00:25Z |
| format | Journal article |
| id | oxford-uuid:271c11e5-0d12-4aae-ab1c-a0b8a02397c7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:00:25Z |
| publishDate | 2021 |
| publisher | Association for Computing Machinery |
| record_format | dspace |
| spelling | oxford-uuid:271c11e5-0d12-4aae-ab1c-a0b8a02397c72022-03-26T12:04:53ZPCPATCH: software for the topological construction of multigrid relaxation methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:271c11e5-0d12-4aae-ab1c-a0b8a02397c7EnglishSymplectic ElementsAssociation for Computing Machinery2021Farrell, PEKnepley, MGMitchell, LWechsung, FEffective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems. |
| spellingShingle | Farrell, PE Knepley, MG Mitchell, L Wechsung, F PCPATCH: software for the topological construction of multigrid relaxation methods |
| title | PCPATCH: software for the topological construction of multigrid relaxation methods |
| title_full | PCPATCH: software for the topological construction of multigrid relaxation methods |
| title_fullStr | PCPATCH: software for the topological construction of multigrid relaxation methods |
| title_full_unstemmed | PCPATCH: software for the topological construction of multigrid relaxation methods |
| title_short | PCPATCH: software for the topological construction of multigrid relaxation methods |
| title_sort | pcpatch software for the topological construction of multigrid relaxation methods |
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