Condition number estimates for the nonoverlapping optimized Schwarz method and the 2-Lagrange multiplier method for general domains and cross points

Research output: Contribution to journalArticle

17 Citations (Scopus)
87 Downloads (Pure)

Abstract

The optimized Schwarz method and the closely related 2-Lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations. Although these methods are known to work well in special cases (e. g., when the domain is a square and the two subdomains are rectangles), the problem has never been systematically stated nor analyzed for general domains with general subdomains. The problem of cross points (when three or more subdomains meet at a single vertex) has been particularly vexing. We introduce a 2-Lagrange multiplier method for domain decompositions with cross points. We estimate the condition number of the iteration and provide an optimized Robin parameter for general domains. We hope that this new systematic theory will allow broader utilization of optimized Schwarz and 2-Lagrange multiplier preconditioners.

Original languageEnglish
Pages (from-to)3062-3083
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number6
DOIs
Publication statusPublished - 2013

Keywords

  • domain decomposition
  • Schwarz method
  • partial differential equation
  • parallel preconditioner
  • Krylov space
  • 2-Lagrange multiplier
  • WAVE-FORM RELAXATION
  • ABSORBING BOUNDARY-CONDITIONS
  • SHALLOW-WATER EQUATIONS
  • DECOMPOSITION METHODS
  • DIFFUSION PROBLEMS

Cite this