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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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 21; no. 3; pp. 709 - 728
Main Authors Witte, Julius, Arndt, Daniel, Kanschat, Guido
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.07.2021
Walter de Gruyter GmbH
Subjects
65N55
65Y20
Differential equations
Discontinuous Galerkin Finite Element
Domain Decomposition
Fast Diagonalization
Finite element method
Galerkin method
Geometric Multigrid
Mathematical analysis
Multigrid methods
Operators (mathematics)
Polynomials
Representations
Tensors
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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 is reduced from to 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
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2020-0078