Robust Preconditioning of Dense Problems from Electromagnetics

Abstract

We consider different preconditioning techniques of both implicit and explicit form in connection with Krylov methods for the solution of large dense complex symmetric non-Hermitian systems of equations arising in computational electromagnetics. We emphasize in particular sparse approximate inverse techniques that use a static nonzero pattern selection. By exploiting geometric information from the underlying meshes, a very sparse but effective preconditioner can be computed. In particular our strategies are applicable when fast multipole methods are used for the matrix-vector products on parallel distributed memory computers.