Sparse pattern selection strategies for robust Frobenius-norm minimizationpreconditioners in electromagnetism

We consider preconditioning strategies for the iterative solution of dense complex symmetric non-Hermitian systems arising in computational electromag netics. We consider in particular sparse approximate inverse preconditioner s that use static non-zero pattern selection. The novelty of our approach c omes from using a different non-zero pattern selection procedure for the or iginal matrix from that for the preconditioner and from exploiting geometri c or topological information from the underlying meshes instead of using me thods based on the magnitude of the entries. The numerical and computationa l efficiency of the proposed preconditioners are illustrated on a set of mo del problems arising both from academic and from industrial applications. T he 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 app licable when fast multipole techniques are used for the matrix-vector produ ct on parallel distributed memory computers. Copyright (C) 2000 John Wiley & Sons, Ltd.