A Nonoverlapping Domain Decomposition Method for Maxwell's Equations in Three Dimensions

Abstract

In this paper, we propose a nonoverlapping domain decomposition method for solving the three-dimensional Maxwell equations, based on the edge element discretization. For the Schur complement system on the interface, we construct an efficient preconditioner by introducing two special coarse subspaces defined on the nonoverlapping subdomains. It is shown that the condition number of the preconditioned system grows only polylogarithmically with the ratio between the subdomain diameter and the finite element mesh size but possibly depends on the jumps of the coefficients.