Efficient Parallelization of the Multilevel Fast Multipole Algorithm for the Solution of Large-Scale Scattering Problems

We present fast and accurate solutions of large-scale scattering problems involving three-dimensional closed conductors with arbitrary shapes using the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA, scattering problems that are discretized with tens of millions of unknowns are easily solved on a cluster of computers. We extensively investigate the parallelization of MLFMA, identify the bottlenecks, and provide remedial procedures to improve the efficiency of the implementations. The accuracy of the solutions is demonstrated on a scattering problem involving a sphere of radius discretized with 41 883 638 unknowns, the largest integral-equation problem solved to date. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions.