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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Bibliographic Details
Published in:Journal of parallel and distributed computing Vol. 70; no. 7; pp. 779 - 782
Main Authors: Chen, Wenwu, Poirier, Bill
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.07.2010
Elsevier
Subjects:
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
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
ISSN:0743-7315, 1096-0848
Online Access:Get full text
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Summary: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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ISSN:0743-7315
1096-0848
DOI:10.1016/j.jpdc.2010.03.008