Multipole-to-local operator in the Fast Multipole Method: comparison of FFT, rotations and BLAS improvements
| hal.structure.identifier | Algorithms and high performance computing for grand challenge applications [SCALAPPLIX] | |
| dc.contributor.author | FORTIN, Pierre | |
| dc.date.accessioned | 2024-04-15T09:45:21Z | |
| dc.date.available | 2024-04-15T09:45:21Z | |
| dc.date.created | 2005-11 | |
| dc.date.issued | 2005-11 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/197911 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | FAST MULTIPOLE METHOD | |
| dc.subject.en | UNIFORM DISTRIBUTION | |
| dc.subject.en | ERROR BOUND | |
| dc.subject.en | FAST FOURIER TRANSFORM | |
| dc.subject.en | ROTATION | |
| dc.subject.en | BLAS | |
| dc.title.en | Multipole-to-local operator in the Fast Multipole Method: comparison of FFT, rotations and BLAS improvements | |
| dc.type | Rapport | |
| dc.subject.hal | Informatique [cs]/Autre [cs.OH] | |
| bordeaux.page | 65 | |
| bordeaux.hal.laboratories | Laboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.type.institution | INRIA | |
| hal.identifier | inria-00070267 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00070267v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2005-11&rft.spage=65&rft.epage=65&rft.au=FORTIN,%20Pierre&rft.genre=unknown |
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