A Novel Algorithm for Large-Scale Fock Matrix Generation with Small Local Distributed Memory Parallel Architecture.
- Relation to the Integral Cutoff -

Hajime TAKASHIMAa, So YAMADAb, Shigeru OBARAc, Kunihiro KITAMURAa, Shinjiro INABATAb, Nobuaki MIYAKAWAb, Kazutoshi TANABEd and Umpei NAGASHIMAe*

aTaisho Pharmaceutical Co. Ltd.
1-403 Yoshino, Ohmiya, Saitama 330-8530, Japan
bFuji Xerox Co. Ltd.
2274 Hongo, Ebina, Kanagawa 243-0494, Japan
cHokkaido University of Education
1-15-55 Shiroyama, Kushiro Hokkaido, 085-8580, Japan
dNational Institute of Materials and Chemical Reactions
1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
eNational Institute for Advanced Interdisciplinary Research
1-1-4 Higashi, Tsukuba, Ibaraki 305-8562, Japan

(Received: December 10, 1999; Accepted for publication: January 7, 2000; Published on Web: April 10, 2000)

We are now developing a special purpose machine for accelerating ab initio molecular orbital calculations, MOEngine, a parallel architecture with small local distributed memories. This machine enables low-cost and high-performance molecular orbital calculations. MOEngine has such small memories, several megabytes, for each processor that all the matrix elements cannot be put on each memory. Conventional Fock matrix construction algorithms cannot be applied for MOEngine, and a new parallel distributed algorithm is required in which matrix element data are transferred between a host machine and each processor whenever it is necessary. Then, we developed a novel algorithm for large-scale Fock matrix generation with small local distributed memory parallel architecture. In this paper, we give a detailed explanation of "cutoff", and descrive the relationship between the "cutoff" and a Fock matrix generation algorithm for small distributed memory. In such an algorithm, "matrix element cutoff" which cooperates with the integral cutoff is indispensable for the decrease of the amount of data transfer. We have also investigated how much integral cutoff is done in large molecules. The ratio of the cutoff-survival basis number to the original basis number is less than 10%, and the survival basis number becomes nearly constant. This means that, in large molecules, the number of effective electron repulsion integrals decreases remarkably and is proportional to the order of N2.

Keywords: Distributed Memory Parallel Computer, Ab Initio Molecular Orbital Calculation, Fock Matrix Generation, Integral Cutoff

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