### Abstract

The linear solve problems arising in chemical physics and many other fields involve large sparse matrices with a certain block structure, for which special block Jacobi preconditioners are found to be very efficient. In two previous papers [W. Chen, B. Poirier, Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. I. Block Jacobi diagonalization, J. Comput. Phys. 219 (1) (2006) 185197; W. Chen, B. Poirier, Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. II. QMR linear solver, J. Comput. Phys. 219 (1) (2006) 198209], a parallel implementation was presented. Excellent parallel scalability was observed for preconditioner construction, but not for the matrixvector product itself. In this paper, we introduce a new algorithm with (1) greatly improved parallel scalability and (2) generalization for arbitrary number of nodes and data sizes.

Original language | English |
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Pages (from-to) | 779-782 |

Number of pages | 4 |

Journal | Journal of Parallel and Distributed Computing |

Volume | 70 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2010 |

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### Keywords

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

### Cite this

*Journal of Parallel and Distributed Computing*,

*70*(7), 779-782. https://doi.org/10.1016/j.jpdc.2010.03.008