## Abstract

Linear systems in chemical physics often involve matrices with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix-vector products) in conjunction with a block Jacobi preconditioner [Numer. Linear Algebra Appl. 7 (2000) 715]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements. The present study (paper I) emphasizes construction of the block Jacobi preconditioner matrices. This is achieved in a preprocessing step, performed prior to the subsequent iterative linear solve step, considered in a companion paper (paper II). Results indicate that the block Jacobi routines scale remarkably well on parallel computing platforms, and should remain effective over tens of thousands of nodes.

Original language | English |
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Pages (from-to) | 185-197 |

Number of pages | 13 |

Journal | Journal of Computational Physics |

Volume | 219 |

Issue number | 1 |

DOIs | |

State | Published - Nov 20 2006 |

## Keywords

- Block Jacobi
- Chemical physics
- Eigensolver
- Linear solver
- Parallel computing
- Preconditioning
- Sparse matrix