#### Juan G. Calvo

#### 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 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.