Some Sparse Pattern Selection Strategies for Robust Frobenius Norm MinimizationPreconditioners in Electromagnetism

摘要

The authors consider preconditioning strategies for the iterative solution ofdense complex symmetric non-Hermitian systems arising in computational electromagnetics. The authors consider in particular sparse approximate inverse preconditioners that use a static nonzero pattern selection. The novelty of the authors' approach comes from using a different nonzero 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 efficiency of the propose 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, the authors' strategies are applicable when fast multipole techniques are used for the matrix-vector product on parallel distributed memory computers.