Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method

Eric T. Chung; Hyea Hyun Kim; Olof B. Widlund

doi:10.1137/110849432

Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method

Eric T. Chung, Hyea Hyun Kim, Olof B. Widlund

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Two overlapping Schwarz algorithms are developed for a discontinuous Galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions. The discontinuous Galerkin formulation is based on a staggered discretization introduced by Chung and Engquist [SIAM J. Numer. Anal., 47 (2009), pp. 3820-3848] for the acoustic wave equation. Two types of coarse problems are introduced for the two-level Schwarz algorithms. The first is built on a nonoverlapping subdomain partition, which allows quite general subdomain partitions, and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation. Condition number bounds are established and numerical results are presented.

Original language	English (US)
Pages (from-to)	47-67
Number of pages	21
Journal	SIAM Journal on Numerical Analysis
Volume	51
Issue number	1
DOIs	https://doi.org/10.1137/110849432
State	Published - 2013

Keywords

Discontinuous Galerkin methods
Domain decomposition
Elliptic problems
Overlapping Schwarz algorithms
Preconditioned conjugate gradients
Staggered grids

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/110849432

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abstract = "Two overlapping Schwarz algorithms are developed for a discontinuous Galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions. The discontinuous Galerkin formulation is based on a staggered discretization introduced by Chung and Engquist [SIAM J. Numer. Anal., 47 (2009), pp. 3820-3848] for the acoustic wave equation. Two types of coarse problems are introduced for the two-level Schwarz algorithms. The first is built on a nonoverlapping subdomain partition, which allows quite general subdomain partitions, and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation. Condition number bounds are established and numerical results are presented.",

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AU - Kim, Hyea Hyun

AU - Widlund, Olof B.

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N2 - Two overlapping Schwarz algorithms are developed for a discontinuous Galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions. The discontinuous Galerkin formulation is based on a staggered discretization introduced by Chung and Engquist [SIAM J. Numer. Anal., 47 (2009), pp. 3820-3848] for the acoustic wave equation. Two types of coarse problems are introduced for the two-level Schwarz algorithms. The first is built on a nonoverlapping subdomain partition, which allows quite general subdomain partitions, and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation. Condition number bounds are established and numerical results are presented.

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Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method

Abstract

Keywords

ASJC Scopus subject areas

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