Abstract
In this paper the parallel algorithm of preconditioned conjugate gradient method (PCGM) is presented and implemented on DELL workstation cluster. Optimization techniques for the sparse matrix vector multiplication are adopted in programming. The storage schemes are analyzed in detail. The numerical results show that the designed parallel algorithm has good parallel performance on the high performance workstation cluster. This illustrates the power of parallel computing in solving large-scale problems much faster than on a single processor.
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References
Barret, R., et al.: Templates for the Solution of Linear Systems, Building Blocks for Iterative Methods. SIAM, Philadelphia (1994)
Law, K.H.: A Parallel Finite Element Solution Method. Computers & Structures, 23(6), 845–858 (1986)
George, E.K., et al.: Parallel Scientific Computing in C++ and MPI. Cambridge University Press (2003)
Pacheco, P.S.: Parallel Programming with MPI. Morgan Kaufmann (1997)
Allen, K.P.: Efficient Parallel Computing for Solving Linear Systems of Equations. Graduate Student Seminar, University of Maryland, Baltimore County (2003)
Brown, P.N., Hindmarsh, A.C.: Matrix-free methods for stiff systems of ODE’s. SIAM J. Numer, Anal, 23, 610–638 (1986)
Sorin, G.N., et al.: Load-Balanced Sparse Matrix-Vector Multiplication on Parallel Computers. Parallel and Distributed Computing, 46, 180–193 (1997)
Aliaga, J.I., Hernandez, V.: Symmetric sparse matrix-vector product on distributed memory multiprocessors. Conference on Parallel Computing and Transputer Applications, Barcelona, Spain (1992)
Ortigosa, E.M., et al.: Parallel scheduling of the PCG method for banded matrices rising from FDM/FEM. J. Parallel Distrib. Comput., 63, 1243–1256 (2003)
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© 2005 Springer-Verlag Berlin Heidelberg
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Fu, C., Zhang, W., Yang, L. (2005). Parallel Computing for Linear Systems of Equations on Workstation Clusters. In: Zhang, W., Tong, W., Chen, Z., Glowinski, R. (eds) Current Trends in High Performance Computing and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27912-1_33
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DOI: https://doi.org/10.1007/3-540-27912-1_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25785-1
Online ISBN: 978-3-540-27912-9
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