TY - GEN

T1 - Accomodating irregular subdomains in domain decomposition theory

AU - Widlund, Olof B.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78651586748&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-02677-5_8

DO - 10.1007/978-3-642-02677-5_8

M3 - Conference contribution

AN - SCOPUS:78651586748

SN - 9783642026768

T3 - Lecture Notes in Computational Science and Engineering

SP - 87

EP - 98

BT - Domain Decomposition Methods in Science and Engineering XVIII

T2 - 18th International Conference of Domain Decomposition Methods

Y2 - 12 January 2008 through 17 January 2008

ER -