## A two-level overlapping Schwarz method for H(curl) in two dimensions with irregular subdomains

Juan G. Calvo

### Abstract

A bound is obtained for the condition number of a two-level overlapping Schwarz algorithm for problems posed in $H({\rm curl})$ in two dimensions, where the subdomains are only assumed to be John subdomains. The coarse space is based on energy minimization and its dimension equals the number of interior subdomain edges. Local direct solvers are used on the overlapping subdomains. Our bound depends only on a few geometric parameters of the decomposition. This bound is independent of jumps in the coefficients across the interface between the subdomains for most of the different cases considered. Numerical experiments that verify the result are shown, including some with subdomains with fractal edges and others obtained by a mesh partitioner.

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### Key words

Domain decomposition, overlapping Schwarz algorithms, preconditioners, irregular subdomain boundaries, $H$(curl), Maxwell's equations, discontinuous coefficients

### AMS subject classifications

65N55, 65N30, 65F10, 35Q60

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