An overlapping preconditioner for 2D virtual problems posed in H(rot) with irregular subdomains

Abstract

We present a two-level overlapping Schwarz preconditioner for problems posed in H(rot) in two dimensions, that extends previous methods for Nédélec elements (triangular meshes) to general polygonal partitions (virtual methods). The coarse space is based on virtual spaces and its dimension equals the number of subdomain edges. Moreover, for the interpolation from coarse to fine mesh, instead of using discrete harmonic extensions, we include the description of a method based on polynomial projectors, related to virtual element methods. We include numerical results that confirm our method is competitive.