A Parallel Directional Fast Multipole Method.
SIAM JOURNAL ON SCIENTIFIC COMPUTING(2014)
摘要
This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We propose a simple partition at a fixed level of the octree and show that, if the partitions are properly balanced between p processes, the overall runtime is essentially O N log N/p + p. By the structure of the low-rank criterion, we are able to avoid communication at the top of the octree. We demonstrate the effectiveness of our parallelization on several challenging models.
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关键词
parallel,fast multipole methods,N-body problems,scattering problems,Helmholtz equation,oscillatory kernels,directional,multilevel
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