A parallel directional Fast Multipole Method

A parallel directional Fast Multipole Method

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-freque...

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Veröffentlicht in:arXiv.org 2013-11
Hauptverfasser: Benson, Austin R, Poulson, Jack, Tran, Kenneth, Engquist, Björn, Lexing Ying
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Sprache:eng
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Computer Science - Numerical Analysis
Criteria
Kernels
Mathematics - Numerical Analysis
Multipoles
Octrees
Partitions
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Poulson, Jack
Tran, Kenneth
Engquist, Björn
Lexing Ying
description 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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subjects Computer Science - Numerical Analysis
Criteria
Kernels
Mathematics - Numerical Analysis
Multipoles
Octrees
Partitions
title A parallel directional Fast Multipole Method
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