Title: Domain Decomposition for Less Regular Subdomains: Overlapping Schwarz in Two Dimensions
(NYU-CS-TR888)
Authors: Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund
Abstract:
In the theory of domain decomposition methods, it is often assumed that each subdomain is the
union of a small set of coarse triangles or tetrahedra. In this study, extensions to the existing
theory which accommodates subdomains with much less regular shape are presented; the subdomains
are only required to be John domains. Attention is focused on overlapping Schwarz preconditioners
for problems in two dimensions with a coarse space component of the preconditioner which allows
for good results even for coefficients which vary considerably. It is shown that the condition number
of the domain decomposition method is bounded by *C*(1 + *H*/δ)(1 + log(*H*/*h*))^{2}, where the constant *C*
independent of the number of subdomains and possible jumps in coefficients between subdomains.
Numerical examples are provided which confirm the theory and demonstrate very good performance
of the method for a variety of subregions including those obtained when a mesh partitioner is
used for the domain decomposition.