Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism

We consider preconditioning strategies for the iterative solution of dense complex symmetric nonHermitian systems arising in computational electromagnetics. We consider in particular sparse approximate inverse preconditioners that use a static nonzero pattern selection. The novelty of our approach comes from using a di erent nonzero pattern selection for the original matrix from that for the preconditioner and from exploiting geometric or topological information from the underlying meshes instead of using methods based on the magnitude of the entries. The numerical and computational e ciency of the proposed preconditioners are illustrated on a set of model problems arising both from academic and from industrial applications. The results of our numerical experiments suggest that the new strategies are viable approaches for the solution of large-scale electromagnetic problems using preconditioned Krylov methods. In particular, our strategies are applicable when fast multipole techniques are used for the matrix-vector product on parallel distributed memory computers.