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

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)47-67
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number1
DOIs
StatePublished - 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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