Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations

Abstract

Time harmonic Maxwell equations in lossless media lead to a secondorder differential equation for the electric field involving a differentialoperator that is neither elliptic nor definite. A Galerkin methodusing Nedelec spaces can be employed to get approximate solutionsnumerically. The problem of preconditioning the indefinite matrixarising from this method is discussed here. Specifically, two overlappingSchwarz methods will be shown to yield uniform preconditioners.