Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems

Marc Garbey, Hans G. Kaper

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problems. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The subdomains match the domains of validity of the local (inner and outer) asymptotic expansions, and cut-off functions are used to match solutions in neighboring subdomains. The positions of the interfaces, as well as the mesh widths, depend on the small parameter ∈. On the subdomains, iterative solution techniques are used, which may vary from one subdomain to another. The global convergence rate depends on ∈; it generally increases like some power of (log(∈-1))-1 as ∈ ↓ 0. The method is illustrated on several two-dimensional singular perturbation problems.

Original languageEnglish (US)
Pages (from-to)1513-1544
Number of pages32
JournalSIAM Journal on Numerical Analysis
Volume34
Issue number4
DOIs
StatePublished - 1997

Keywords

  • Asymptotic analysis
  • Boundary layers
  • Domain decomposition
  • Elliptic boundary value problems
  • Iterative methods
  • Singular perturbations
  • Transition layers
  • Turning-point problems

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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