Fast tensor product Schwarz smoothers for high-order discontinuous Galerkin methods
We discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high-order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices associated to mesh cells and to the patches around a vertex, respectively, in...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Computational methods in applied mathematics
Year: 2021, Volume: 21, Issue: 3, Pages: 709-728 |
| ISSN: | 1609-9389 |
| DOI: | 10.1515/cmam-2020-0078 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1515/cmam-2020-0078 Verlag, lizenzpflichtig, Volltext: https://www.degruyterbrill.com/document/doi/10.1515/cmam-2020-0078/html 
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| Author Notes: | Julius Witte, Daniel Arndt, and Guido Kanschat |
| Summary: | We discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high-order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices associated to mesh cells and to the patches around a vertex, respectively, in order to obtain fast local solvers for additive and multiplicative subspace correction methods. The effort of inverting local matrices for tensor product polynomials of degree k is reduced from 𝒪 ( k 3 d ) {\mathcal{O}(k^{3d})} to 𝒪 ( d k d + 1 ) {\mathcal{O}(dk^{d+1})} by exploiting the separability of the differential operator and resulting low rank representation of its inverse as a prototype for more general low rank representations in space dimension d . |
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| Item Description: | Veröffentlicht von De Gruyter 11. November 2020 Gesehen am 29.09.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1609-9389 |
| DOI: | 10.1515/cmam-2020-0078 |