Parallel implementation of an efficient preconditioned linear solver for grid-based applications in chemical physics. III: Improved parallel scalability for sparse matrix–vector products
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 p...
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| Published in: | Journal of parallel and distributed computing Vol. 70; no. 7; pp. 779 - 782 |
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| 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) 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. |
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| AbstractList | 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. |
| Author | Chen, Wenwu Poirier, Bill |
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| Cites_doi | 10.1016/j.jpdc.2004.12.001 10.1002/1099-1506(200010/12)7:7/8<715::AID-NLA220>3.0.CO;2-R 10.1063/1.462100 10.1063/1.475958 10.1016/j.jcp.2006.03.031 10.1063/1.1367396 10.1016/S0167-8191(01)00073-4 10.1007/BF01385726 10.1016/S0167-8191(00)00027-2 10.1006/jpdc.1996.0051 10.1016/S0009-2614(96)01408-X 10.1016/j.jpdc.2005.12.009 10.1016/j.jcp.2006.04.012 10.1006/jpdc.1996.0011 10.1063/1.1428752 10.1103/PhysRevA.56.120 |
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| Keywords | Parallel computing Eigensolver Block Jacobi Matrix–vector product Linear solver Sparse matrix Chemical physics Preconditioning Matrix diagonalization High performance Parallel algorithm Scalability Physical chemistry Grid Matrix product Jacobi matrix Distributed computing Lanczos method Parallel processing Matrix-vector product Block matrix |
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| References | Gupta, Kaushik, Huang, Sadayappan (b11) 1996; 32 Gupta, Huang, Sadayappan, Johnson (b10) 1996; 34 Geus, Röllin (b7) 2001; 27 Poirier (b14) 1998; 108 Chen, Poirier (b4) 2006; 219 Bertrand, Bramley, Bernholdt, Kohl, Sussman, Larson, Damevski (b1) 2006; 66 Guo, Nakata, Yamashita (b8) 2000; 26 Colbert, Miller (b5) 1992; 96 Guo, Pan (b9) 2005; 65 Boyd (b2) 1989 Poirier, Carrington (b16) 2002; 116 Freund, Nachtigal (b6) 1991; 60 Chen, Poirier (b3) 2006; 219 Poirier (b12) 1997; 56 Poirier, Miller (b17) 1997; 265 Poirier (b13) 2000; 7 Poirier, Carrington (b15) 2001; 114 Poirier (10.1016/j.jpdc.2010.03.008_b13) 2000; 7 Poirier (10.1016/j.jpdc.2010.03.008_b14) 1998; 108 Poirier (10.1016/j.jpdc.2010.03.008_b15) 2001; 114 Poirier (10.1016/j.jpdc.2010.03.008_b16) 2002; 116 Gupta (10.1016/j.jpdc.2010.03.008_b11) 1996; 32 Chen (10.1016/j.jpdc.2010.03.008_b3) 2006; 219 Geus (10.1016/j.jpdc.2010.03.008_b7) 2001; 27 Poirier (10.1016/j.jpdc.2010.03.008_b12) 1997; 56 Guo (10.1016/j.jpdc.2010.03.008_b9) 2005; 65 Gupta (10.1016/j.jpdc.2010.03.008_b10) 1996; 34 Bertrand (10.1016/j.jpdc.2010.03.008_b1) 2006; 66 Freund (10.1016/j.jpdc.2010.03.008_b6) 1991; 60 Colbert (10.1016/j.jpdc.2010.03.008_b5) 1992; 96 Boyd (10.1016/j.jpdc.2010.03.008_b2) 1989 Guo (10.1016/j.jpdc.2010.03.008_b8) 2000; 26 Chen (10.1016/j.jpdc.2010.03.008_b4) 2006; 219 Poirier (10.1016/j.jpdc.2010.03.008_b17) 1997; 265 |
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| SubjectTerms | Algorithms Applied sciences Block Jacobi Blocking Chemical physics Chemistry Computer networks Computer science; control theory; systems Computer systems and distributed systems. User interface Construction Distributed processing Eigensolver Exact sciences and technology General and physical chemistry Linear solver Matrix–vector product Parallel computing Preconditioning Software Solvers Sparse matrices Sparse matrix Theory of reactions, general kinetics Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry |
| Title | Parallel implementation of an efficient preconditioned linear solver for grid-based applications in chemical physics. III: Improved parallel scalability for sparse matrix–vector products |
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