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# Multipole-to-local operator in the Fast Multipole Method: comparison of FFT, rotations and BLAS improvements

1 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
INRIA Futurs, Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : In the Fast Multipole Method, most of the far field computation is due to the multipole-to-local (M2L) operator. In this report we distinguish two different expressions for this operator: while the first one is natural and efficient, and thus commonly used, the second one, unlike the first, respects a sharp error bound, which is proven here. Two schemes, that reduce the operation count of the M2L operator, are detailed: the (block) Fast Fourier Transform and the rotations. We then present a matrix approach that uses BLAS (Basic Linear Algebra Subprograms) routines to speed up the $M2L$ computation. In order to use the more efficient level 3 BLAS (for matrix products), we require recopies, but this additional cost can be avoided thanks to special data storages. Finally all these schemes are compared, theorically and practically with uniform distributions, which validates our BLAS version.
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https://hal.inria.fr/inria-00070267
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Submitted on : Friday, May 19, 2006 - 7:47:20 PM
Last modification on : Friday, February 4, 2022 - 3:22:42 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:47:13 PM

### Identifiers

• HAL Id : inria-00070267, version 1

### Citation

Pierre Fortin. Multipole-to-local operator in the Fast Multipole Method: comparison of FFT, rotations and BLAS improvements. RR-5752, INRIA. 2005, pp.65. ⟨inria-00070267⟩

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