Two-level Overlapping Schwarz Method for H(curl) in 2d for Irregular Subdomains

A bound is obtained for the condition number of a two-level overlapping Schwarz algorithm for problems posed in H(curl) in 2D, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of subdomain edges. Local direct solvers over overlapping subdomains are also used. The bound is independent of jumps in the coefficients across the interface between the subdomains and depends only on a few geometric parameters of the decomposition. Numerical results that verify the result are shown, including some with subdomains with fractal edges and others obtained by a mesh partitioner.