In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with...In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete （RCC） gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.展开更多
The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional ...The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.50808066)
文摘In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete （RCC） gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.
基金supported by the National Natural Science Foundation of China(No.10771031)the Fundamental Research Funds for Central Universities(No.090405013)
文摘The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.
