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New Iterative Method for Solving the Monoenergetic Diffusion Equation with Large Number of Unknowns Using Group Theory

机译:用群论求解具有大量未知数的单能扩散方程的新迭代法

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A new iterative method for solving the monoenergetic diffusion equation is presented. The experience has shown, that the usual iterative methods used to solve the resulting equations either do not converge at all or the number of inner iterations becomes too large when a high order approximation is used for the spatial flux. The aim has been therefore to develop a new iterative method which leads to small number of iterations even for high order of spatial flux approximation. The present method is additionally accelerated using Chebyshev, Wagner and Andrzejewski procedures which are compared. The SAPHIR Benchmark Test case with a fixed volume source was used for calculations because it is difficult to converge. It is shown that the present method needs for Lagrangian flux approximation of 1st to 4th order almost the same number of iterations which is smaller than 53. Chebyshev acceleration which was the most effective, halved the number of inner iterations. (ERA citation 07:059537)

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