Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps

Victorita Dolean Maini, Frederic Nataf, R. Scheichl, N. Spillane

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. For smooth problems, the theory and practice of such two-level methods is well established, but this is not the case for problems with complicated variation and high contrasts in the coefficients. In a previous study, two of the authors introduced a coarse space adapted to highly heterogeneous coefficients using the low frequency modes of the subdomain DtN maps. In this work, we present a rigorous analysis of a two-level overlapping additive Schwarz method with this coarse space, which provides an automatic criterion for the number of modes that need to be added per subdomain to obtain a convergence rate of the order of the constant coefficient case. Our method is suitable for parallel implementation and its efficiency is demonstrated by numerical examples on some challenging problems with high heterogeneities for automatic partitionings.
LanguageEnglish
Pages391–414
Number of pages24
JournalComputational Methods in Applied Mathematics
Volume12
Issue number4
DOIs
Publication statusPublished - 1 Jan 2012
Externally publishedYes

Fingerprint

Two-level Method
Schwarz Methods
Dirichlet-to-Neumann Map
Domain decomposition methods
Coefficient
Additive Schwarz Method
Domain Decomposition Method
Parallel Implementation
Overlapping
Low Frequency
Partitioning
Rate of Convergence
Grid
Numerical Examples

Keywords

  • coarse spaces
  • overlapping Schwarz method
  • eigenvectors

Cite this

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Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps. / Dolean Maini, Victorita; Nataf, Frederic; Scheichl, R.; Spillane, N.

In: Computational Methods in Applied Mathematics, Vol. 12, No. 4, 01.01.2012, p. 391–414.

Research output: Contribution to journalArticle

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