Solutions of large integral-equation problems with preconditioned MLFMA

Abstract

We report the solution of the largest integral-equation problems in computational electromagnetics. We consider matrix equations obtained from the discretization of the integral-equation formulations that are solved iteratively by employing parallel multilevel fast multipole algorithm (MLFMA). With the efficient parallelization of MLFMA, scattering and radiation problems with millions of unknowns are easily solved on relatively inexpensive computational platforms. For the iterative solutions of the matrix equations, we are able to obtain accelerated convergence even for ill-conditioned matrix equations using advanced preconditioning schemes, such as nested preconditioned based on an approximate MLFMA. By orchestrating these diverse activities, we have been able to solve a closed geometry formulated with the CFIE containing 33 millions of unknowns and an open geometry formulated with the EFIE containing 12 millions of unknowns, which are the largest problems of their classes, to the best of our knowledge.