A parallel directional Fast Multipole Method

Abstract

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.

References in corpus (4)

• Minimizing Communication in Linear Algebra
• A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems
• Hierarchical N-body simulations with auto-tuning for heterogeneous systems
• Fourier Based Fast Multipole Method for the Helmholtz Equation

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