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Sparse matrix multiplications for linear scaling electronic structure calculations in an atom‐centered basis set using multiatom blocks
Author(s) -
Saravanan Chandra,
Shao Yihan,
Baer Roi,
Ross Philip N.,
Head–Gordon Martin
Publication year - 2003
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.10224
Subject(s) - scaling , linear scale , basis set , basis (linear algebra) , set (abstract data type) , matrix (chemical analysis) , atom (system on chip) , multidimensional scaling , computer science , algorithm , mathematics , physics , chemistry , quantum mechanics , molecule , parallel computing , geometry , geodesy , chromatography , geography , machine learning , programming language
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. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 618–622, 2003