A BDDC algorithm with deluxe scaling for H(curl) in two dimensions with irregular subdomains

Abstract

A bound is obtained for the condition number of a BDDC algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. For the primal variable space, a continuity constraint for the tangential average over each interior subdomain edge is imposed. For the averaging operator, a new technique named deluxe scaling is used. Our optimal 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.