TY - JOUR

T1 - Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks

AU - Saravanan, Chandra

AU - Shao, Yihan

AU - Baer, Roi

AU - Ross, Philip N.

AU - Head-Gordon, Martin

PY - 2003/4/15

Y1 - 2003/4/15

N2 - A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package.

AB - A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package.

KW - Electronic structure calculations

KW - Linear scaling

KW - Multiatom blocks

UR - http://www.scopus.com/inward/record.url?scp=0037447290&partnerID=8YFLogxK

U2 - 10.1002/jcc.10224

DO - 10.1002/jcc.10224

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AN - SCOPUS:0037447290

SN - 0192-8651

VL - 24

SP - 618

EP - 622

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

IS - 5

ER -