Premium
Two‐electron integral evaluation on the graphics processor unit
Author(s) -
Yasuda Koji
Publication year - 2008
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20779
Subject(s) - computer science , speedup , graphics , computational science , graphics processing unit , algorithm , parallel computing , computer graphics (images)
Abstract We propose the algorithm to evaluate the Coulomb potential in the ab initio density functional calculation on the graphics processor unit (GPU). The numerical accuracy required for the algorithm is investigated in detail. It is shown that GPU, which supports only the single‐precision floating number natively, can take part in the major computational tasks. Because of the limited size of the working memory, the Gauss‐Rys quadrature to evaluate the electron repulsion integrals (ERIs) is investigated in detail. The error analysis of the quadrature is performed. New interpolation formula of the roots and weights is presented, which is suitable for the processor of the single‐instruction multiple‐data type. It is proposed to calculate only small ERIs on GPU. ERIs can be classified efficiently with the upper‐bound formula. The algorithm is implemented on NVIDIA GeForce 8800 GTX and the Gaussian 03 program suite. It is applied to the test molecules Taxol and Valinomycin. The total energies calculated are essentially the same as the reference ones. The preliminary results show the considerable speedup over the commodity microprocessor. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008