Overlapping Schwarz methods in H(curl) on polyhedron domains

Joseph E. Pasciak and Jun Zhao

Department of Mathematics, Texas A&M University, College Station, TX 77843


Abstract

Time-dependent Maxwell equations lead to a second order differential equation for the electric field. A Galerkin method using Nedelec elements can be employed to solve this problem numerically. The condition number of the resulting linear algebraic equation depends on both the mesh and the time step size.

In this talk, I will give an analysis of overlapping Schwarz methods for preconditioning the linear systems arising from the above mentioned discretizations for problems posed on nonconvex domains. First, the theory for Schwarz preconditioning of the 2nd order elliptic problem will be reviewed. Next, some earlier results for Schwarz methods applied to Maxwell's equations on convex domains will be discussed. The talk will conclude with a sketch of the proof in the nonconvex case.