Accomodating irregular subdomains in domain decomposition theory

Olof B. Widlund

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XVIII
Number of pages12
StatePublished - 2009
Event18th International Conference of Domain Decomposition Methods - Jerusalem, Israel
Duration: Jan 12 2008Jan 17 2008

Publication series

NameLecture Notes in Computational Science and Engineering
Volume70 LNCSE
ISSN (Print)1439-7358


Other18th International Conference of Domain Decomposition Methods

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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