Sparse pattern selection strategies for robust Frobenius norm minimization preconditioners in electromagnetism
by
Bruno Carpentieri
CERFACS - Toulouse, France
Coauthors: Iain S. Duff (Rutherford Appleton Laboratory), Luc Giraud (CERFACS)

We consider preconditioning strategies for the iterative solution of dense
complex symmetric non-Hermitian 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 different nonzero pattern selection for the original matrix than for the preconditioner and from exploiting geometrical or topological information from
the underlying meshes in addition to using methods based on the magnitude of
the entries. The numerical and computational efficiency of the proposed preconditioners are illustrated on a set of model problems arising both from academic and from industrial applications. Our numerical experiments, compared
to those observed with some classical preconditioners of both explicit and implicit form, suggest that the new strategies are viable approaches for the solution of large-scale electromagnetic problems using preconditioned Krylov methods. In particular our strategies exploit only physical informations related to the near field, so that they are applicable when fast multipole techniques
are used for the matrix-vector product on parallel distributed memory computers.

Date received: January 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-30.