Iterative techniques for mixed discretizations of Maxwells equations.

Joseph E. Pasciak

Abstract:

Maxwell equations in lossless media leads to a second order differential equation for the electric field that is not elliptic, and is indefinite. This is a variational system involving an indefinite bilinear form in H(curl). The Galerkin discretization based on Nedelec spaces has been show to provide accurate approximate solutions. In this talk, the issue of preconditioning the indefinite matrix arising from this method will be discussed. Specifically, the overlapping Schwarz method will be shown to give rise to an iterative scheme converging at a rate which independent of the the mesh size.