COULAUD, Olivier; FORTIN, Pierre; ROMAN, Jean

doi:10.1016/j.jcp.2007.09.027

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COULAUD, Olivier
Algorithms and high performance computing for grand challenge applications [SCALAPPLIX]

FORTIN, Pierre
Algorithms and high performance computing for grand challenge applications [SCALAPPLIX]

ROMAN, Jean
Algorithms and high performance computing for grand challenge applications [SCALAPPLIX]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]

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Journal of Computational Physics. 2008, vol. 227, n° 3, p. 1836-1862

Elsevier

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The multipole-to-local (M2L) operator is the most time-consuming part of the far field computation in the Fast Multipole Method for Laplace equation. Its natural expression, though commonly used, does not respect a sharp error bound: we here first prove the correctness of a second expression. We then propose a matrix formulation implemented with BLAS (Basic Linear Algebra Subprograms) routines in order to speed up its computation for these two expressions. We also introduce special data storages in memory to gain greater computational efficiency. This BLAS scheme is finally compared, for uniform distributions, to other M2L improvements such as block FFT, rotations and plane wave expansions. When considering runtime, extra memory storage, numerical stability and common precisions for Laplace equation, the BLAS version appears as the best one.< Réduire

Mots clés en anglais

Fast Multipole Methods

Laplace equation

BLAS routines

error bound

Fast Fourier Transform

rotations

plane waves

uniform distribution

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High performance BLAS formulation of the multipole-to-local operator in the Fast Multipole Method

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