FORTIN, Pierre

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

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2005-11p. 65

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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.< Réduire

Mots clés en anglais

FAST MULTIPOLE METHOD

UNIFORM DISTRIBUTION

ERROR BOUND

FAST FOURIER TRANSFORM

ROTATION

BLAS

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

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