## Abstract

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.

Original language | American English |
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Pages (from-to) | 618-622 |

Number of pages | 5 |

Journal | Journal of Computational Chemistry |

Volume | 24 |

Issue number | 5 |

DOIs | |

State | Published - 15 Apr 2003 |

## Keywords

- Electronic structure calculations
- Linear scaling
- Multiatom blocks