PCPATCH: software for the topological construction of multigrid relaxation methods
| Autor: | Patrick E. Farrell, Lawrence Mitchell, Florian Wechsung, Matthew G. Knepley |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
business.industry Computer science Applied Mathematics Structure (category theory) Relaxation (iterative method) Numerical Analysis (math.NA) 010103 numerical & computational mathematics Solver Topology Computer Science::Numerical Analysis 01 natural sciences 010101 applied mathematics Range (mathematics) Multigrid method Development (topology) Software Saddle point FOS: Mathematics Computer Science - Mathematical Software Mathematics - Numerical Analysis 0101 mathematics business Mathematical Software (cs.MS) |
| Zdroj: | Transactions on Mathematical Software, 2021, Vol.47(3), pp.1-22 [Peer Reviewed Journal] |
| DOI: | 10.1145/3445791 |
| Popis: | Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gau{\ss}-Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this paper 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. Comment: 22 pages, minor fixes in bibliography |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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