Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation

Rio Yokota; Huda Ibeid; David Keyes

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arXiv · 1602.02244

Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation

Rio Yokota·Huda Ibeid·David Keyes

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Abstract

There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.

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BibTeX RIS

Rio Yokota, Huda Ibeid, David Keyes. 2016-02-06. Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation. https://arxiv.org/abs/1602.02244

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