Two-level additive preconditioners for edge element discretizations of time-harmonic Maxwell equations

Abstract

Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl-operator in a fine space to a coarse mesh space, to solve the original problem, and then uses the fine mesh space to solve the H(curl)-elliptic problem. It is shown that the generalized minimal residual (GMRES) method applied to the preconditioned system converges uniformly provided that the coarsest mesh size is reasonably small (but independent of the fine mesh size) and the parameter for the “coarse mesh” space solver is sufficiently large. Numerical experiments show the efficiency of the proposed approach.