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International Journal of High Performance Computing Applications
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Automatic Generation of FFT for Translations of Multipole Expansions in Spherical Harmonics

Jakub Kurzak

Department Of Electrical Engineering and Computer Science,University of Tennessee, Knoxville, Tennessee 37996, kurzak{at}eecs.utk.edu

Dragan Mirkovic

Department of Computer Science, University of Houston, Houston, Texas 77204

B. Montgomery Pettitt

Department of Computer Science, University of Houston, Houston, Texas 77204, Department of Chemistry, University of Houston, Houston, Texas 77204

S. Lennart Johnsson

Department of Computer Science, University of Houston, Houston, Texas 77204

The fast multipole method (FMM) is an efficient algorithm for calculating electrostatic interactions in molecular simulations and a promising alternative to Ewald summation methods. Translation of multipole expansion in spherical harmonics is the most important operation of the fast multipole method and the fast Fourier transform (FFT) acceleration of this operation is among the fastest methods of improving its performance. The technique relies on highly optimized implementation of fast Fourier transform routines for the desired expansion sizes, which need to incorporate the knowledge of symmetries and zero elements in the input arrays. Here a method is presented for automatic generation of such, highly optimized, routines.

Key Words: fast multipole method • particle dynamics • spherical harmonics • fast Fourier transform • automatic code generation

International Journal of High Performance Computing Applications, Vol. 22, No. 2, 219-230 (2008)
DOI: 10.1177/1094342008090915
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