TWO ALGORITHMS are known for solving very large integral-equation problems involving electromagnetic (EM) scattering from conducting bodies: the Fast Multipole Method (FMM) and its multilevel version, the Multilevel Fast Multipole Algorithm (MLFMA). Both algorithms have the ability to cluster the geometry into groups. The interactions between groups at a large distance are approximated using a few multipole expansions in the framework of an iterative resolution of the Method of Moments (MoM). When combined with a smart parallelization strategy, the scaling properties of the FMM-Fast Fourier Transform (FFT) were recently shown to be very effective when using large, parallel supercomputers.
Specifically, a challenging problem with more than 150 million unknowns has been solved by J.M. Taboada and L. Landesa from Spain's Universidad de Extremadura together with F. Obelleiro, J.L. Rodriguez, J.M. Bertolo, and M.G. Araujo from Universidade de Vigo and J.C. Mourio and A. Gomez from Centro de Supercomputacion de Galicia. The researchers demonstrated that the proposed FMM-FFT implementation constitutes a viable alternative to the more frequently used multilevel approaches. Notably, the team achieved high efficiency with 1024 parallel processors.
The method involved the use of an FFT to speed the translation stage in the FMM framework. The researchers were able to implement the efficient parallelization of the FMM-FFT algorithm by leveraging its inherent high scaling properties. They could then take advantage of the availability of massively distributed supercomputers. They considered a three-stage parallelization strategy with different workload distributions for the far- and near-field contributions as well as the iterative solver. See "High Scalability FMMFFT Electromagnetic Solver for Supercomputer Systems," IEEE Antennas And Propagation Magazine, December 2009, p. 20.