Journal
JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
Volume 70, Issue 7, Pages 779-782Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jpdc.2010.03.008
Keywords
Sparse matrix; Preconditioning; Block Jacobi; Matrix-vector product; Chemical physics; Parallel computing; Eigensolver; Linear solver
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Funding
- Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational Sciences Division of the US Department of Energy [DE-FG03-02ER25534]
- Welch Foundation [D-1523]
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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) 185-197; 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) 198-209], a parallel implementation was presented. Excellent parallel scalability was observed for preconditioner construction, but not for the matrix-vector 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. (C) 2010 Elsevier Inc. All rights reserved.
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