| Summary: | 碩士 === 國立清華大學 === 工程與系統科學系 === 96 === Abstract
TORT (Three Dimensional Oak Ridge Discrete Ordinates Neutron/photon Transport Code) is a program for the calculation of the radiation shielding in nuclear power plant and nuclear spent fuel storage. The simulation of TORT relies on the discrete ordinates method known as the Sn method which shifts transport equation to a large linear system. The Numerical method typically used to solve linear systems is SOR (Successive Over-Relaxation) and it had been applied to TORT. Recently, other methods are proposed successfully for TORT, such as the preconditioned CGS (conjugate gradient squared) and the preconditioned BICGSTAB (Biconjugate Gradient Stabilized) with the point-wise incomplete LU factorization (ILU(0)) and modified point-wise incomplete LU factorization (MILU) preconditioners to be used in 32-bit personal computer. In this study, we developed subroutines based on the preconditioned TFQMR (transpose-free quasi-minimal residual) and QMRCGSTAB (Quasi-minimal Residual Biconjugate Gradient Stabilized) to be connected to TORT. In previous studies, the two numerical methods are difficult to converge in 32-bit personal computer. This leads to testing the numerical methods in 64-bit central processing unit (CPU) since more bits in CPU always yields less round off error. Here we test TORT program in AMD ATHLON 64x2 dual-core processor with operational system Mandriva Linux, the 2007 edition. We find that the convergence behaviors of the preconditioned TFQMR and QMRCGSTAB methods with preconditioner ILU(0) are more efficient than those with the preconditioner MILU. Also, the convergences of the preconditioned TFQMR and the preconditioned QMRCGSTAB in the 64-bit personal computer are faster than those in 32-bit personal computer. Moreover, the numerical results are the same as the results obtained from using SOR, CGS or BICGSTAB in TORT with both 32-bit and 64-bit personal computers.
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