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Two-electron integral evaluation on the graphics processor unit

Koji Yasuda
Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan
Journal of Computational Chemistry, Vol. 29, No. 3. (2008), pp. 334-342

@article{yasuda2008two,

   title={Two-electron integral evaluation on the graphics processor unit},

   author={Yasuda, K.},

   journal={Journal of Computational Chemistry},

   volume={29},

   number={3},

   pages={334–342},

   issn={1096-987X},

   year={2008},

   publisher={Wiley Online Library}

}

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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.
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