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
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
本文介绍了基于统一计算设备架构(Compute Unified Device Architecture,CUDA)的图形处理器(Graphic Processing Unit,GPU)计算环境在钍基熔盐堆(Thorium Molten Salt Reactor,TMSR)设计平台的建立,并将反应堆球场计算软件SRAC(Structur...本文介绍了基于统一计算设备架构(Compute Unified Device Architecture,CUDA)的图形处理器(Graphic Processing Unit,GPU)计算环境在钍基熔盐堆(Thorium Molten Salt Reactor,TMSR)设计平台的建立,并将反应堆球场计算软件SRAC(Structure Research and Analysic Corporation)的中子三维扩散计算模块移植到GPU上进行测试及结果验证。采用中心点差分方法推导出三维扩散计算的差分方程,并用超松弛迭代法(Successive Over Relaxation Method,SOR)求解φ,研究了SOR迭代算法的并行实现过程。结果表明,移植的GPU模块部分计算正确,计算速度得到有效提升,验证了TMSR设计平台在GPU计算环境下可正常工作。展开更多
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））.
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.
文摘本文介绍了基于统一计算设备架构(Compute Unified Device Architecture,CUDA)的图形处理器(Graphic Processing Unit,GPU)计算环境在钍基熔盐堆(Thorium Molten Salt Reactor,TMSR)设计平台的建立,并将反应堆球场计算软件SRAC(Structure Research and Analysic Corporation)的中子三维扩散计算模块移植到GPU上进行测试及结果验证。采用中心点差分方法推导出三维扩散计算的差分方程,并用超松弛迭代法(Successive Over Relaxation Method,SOR)求解φ,研究了SOR迭代算法的并行实现过程。结果表明,移植的GPU模块部分计算正确,计算速度得到有效提升,验证了TMSR设计平台在GPU计算环境下可正常工作。
