Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation
arXiv:1602.02244
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.
19 pages, 6 figures
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Cited by in corpus (4)
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- Application of the Fast Multipole Fully Coupled Poroelastic Displacement Discontinuity Method to Hydraulic Fracturing Problems
- FFT, FMM, and Multigrid on the Road to Exascale: performance challenges and opportunities
- A fast direct solver for the advection-diffusion equation using low-rank approximation of the Green's function