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Convergence properties of iterative algorithms for solving the nodal diffusion equations [electronic resource].

Published
Washington, D.C : United States. Dept. of Energy. Office of Energy Research, 1990.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description
Pages: (13 pages) : digital, PDF file
Additional Creators
Oak Ridge National Laboratory, United States. Department of Energy. Office of Energy Research, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary
We drive the five point form of the nodal diffusion equations in two-dimensional Cartesian geometry and develop three iterative schemes to solve the discrete-variable equations: the unaccelerated, partial Successive Over Relaxation (SOR), and the full SOR methods. By decomposing the iteration error into its Fourier modes, we determine the spectral radius of each method for infinite medium, uniform model problems, and for the unaccelerated and partial SOR methods for finite medium, uniform model problems. Also for the two variants of the SOR method we determine the optimal relaxation factor that results in the smallest number of iterations required for convergence. Our results indicate that the number of iterations for the unaccelerated and partial SOR methods is second order in the number of nodes per dimension, while, for the full SOR this behavior is first order, resulting in much faster convergence for very large problems. We successfully verify the results of the spectral analysis against those of numerical experiments, and we show that for the full SOR method the linear dependence of the number of iterations on the number of nodes per dimension is relatively insensitive to the value of the relaxation parameter, and that it remains linear even for heterogenous problems. 14 refs., 1 fig.
Report Numbers
E 1.99:conf-900418-1
conf-900418-1
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Note
Published through SciTech Connect.
01/01/1990.
"conf-900418-1"
"DE89016859"
International conference on the physics of reactors: operation, design and computation, Marseilles (France), 23-26 Apr 1990.
Azmy, Y Y; Kirk, B L.
Funding Information
AC05-84OR21400
View MARC record | catkey: 14749176