Adaptive GDSW coarse spaces for overlapping schwarz methods in three dimensions

Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

A robust two-level overlapping Schwarz method for scalar elliptic model problems with highly varying coefficient functions is introduced. While the convergence of standard coarse spaces may depend strongly on the contrast of the coefficient function, the condition number bound of the new method is independent of the coefficient function. Indeed, the condition number only depends on a user-prescribed tolerance. The coarse space is based on discrete harmonic extensions of vertex, edge, and face interface functions, which are computed from the solutions of corresponding local generalized edge and face eigenvalue problems. The local eigenvalue problems are of the size of the edges and faces of the decomposition, and the eigenvalue problems can be constructed solely from the local subdomain stiffness matrices and the fully assembled global stiffness matrix. The new AGDSW (adaptive generalized Dryja-Smith-Widlund) coarse space always contains the classical GDSW coarse space by construction of the generalized eigenvalue problems. Numerical results supporting the theory are presented for several model problems in three dimensions using structured as well as unstructured meshes and unstructured decompositions.

Original languageEnglish
Pages (from-to)A3045-A3072
JournalSIAM Journal on Scientific Computing
Volume41
Issue number5
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • Adaptive coarse spaces
  • Domain decomposition
  • GDSW
  • Multiscale
  • Overlapping Schwarz

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