Efficient parallelization of the multilevel fast multipole algorithm (MLFMA)

Abstract

It is possible to solve electromagnetics problems several orders of magnitude faster by using MLFMA. Without exaggeration, this means accelerating the solutions by thousands or even millions of times, compared to the Gaussian elimination. However, it is quite difficult to parallelize MLFMA. This is because of the already-too-complicated structure of the MLFMA solver. Recently, we have developed a hierarchical parallelization scheme for MLFMA. This novel parallelization scheme is both efficient and effective. This way, we have been able to parallelize MLFMA over hundreds of processors. By using distributed-memory architectures, this accomplishment translates into an ability to use more memory and to solve much larger problems than it was possible before. Unlike previous parallelization techniques, with the novel hierarchical partitioning strategy, the tree structure of MLFMA is distributed among processors by partitioning both clusters and samples of fields at each level. Due to the improved load-balancing, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. We demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. We present the effectiveness of our algorithm by solving very large scattering problems.