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Optimized M2L Kernels for the Chebyshev Interpolation based Fast Multipole Method

Abstract : A fast multipole method (FMM) for asymptotically smooth kernel functions (1/r, 1/r^4, Gauss and Stokes kernels, radial basis functions, etc.) based on a Chebyshev interpolation scheme has been introduced in [Fong and Darve, 2009]. The method has been extended to oscillatory kernels (eg. Helmholtz kernel) in [Messner et al., 2011]. Beside its generality this FMM turned out to be favorable due to its easy implementation and performance based on intense use of highly optimized BLAS libraries. However, a bottleneck has been the precomputation of the M2L operator and its higher computational intensity compared to other FMM formulations. Here, we present several optimizations for that operator, which is known to be the most costly FMM operator. The most efficient ones do not only reduce the precomputation time by a factor of more than 1000 but they also speed up the matrix-vector product. We conclude with comparisons and numerical validations of all presented optimizations.
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https://hal.inria.fr/hal-00746089
Contributor : Matthias Messner <>
Submitted on : Saturday, October 27, 2012 - 12:50:56 AM
Last modification on : Monday, November 16, 2020 - 10:34:04 AM
Long-term archiving on: : Monday, January 28, 2013 - 2:40:09 AM

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  • HAL Id : hal-00746089, version 1
  • ARXIV : 1210.7292

Citation

Matthias Messner, Bérenger Bramas, Olivier Coulaud, Eric Darve. Optimized M2L Kernels for the Chebyshev Interpolation based Fast Multipole Method. [Research Report] 2012, pp.22. ⟨hal-00746089v1⟩

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