On the convergence of the multigroup, discrete-ordinates solutions for subcritical transport media
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In the multigroup, discrete-ordinates approximations to the linear transport equation, the integration over the directional variable is replaced by a numerical quadrature rule, involving a weighted sum over functional values at selected directions, with the energy dependence discretized by replacing the cross section data by weighted averages over each energy interval. The stability, consistency, and convergence rely fundamentally on the conditions that the maximum fluctuations in the total cross section — and in the expected number of secondary particles arising from each energy level — tend to zero as the energy mesh becomes finer, and as the number of angular nodes becomes infinite. Our analysis is based on using a natural Nyström method of extending the discrete-ordinates, multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ generalizations of the collectively compact operator approximation theory of P. M. Anselone to deduce stability and convergence of the approximates.
KeywordsTotal Cross Section Compact Operator Operator Approximation Secondary Particle Energy Variable
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- P. M. Anselone,Collectivity Compact Operator Approximation Theory, Prentice-Hall, Englewood Cliffs, N. J., 1971.Google Scholar
- M. Borysiewicz -N. Kruszynska,Smoothness of the solution of the 2-D neutron trnsport equation in the polygon region, Atomkemenergie-Kerntechnik,34 (1979), pp. 11–15.Google Scholar
- R. B. Kellogg,Numerical analysis of the neutron transport ebuations, in: Numerical Solution of Partial Differential Equations - III, SYNSPADE 1975, B. Hubbard ed., New York, Academic Press, Inc., 1976.Google Scholar
- R. T.Rockafellar,Convex Analysis, 1st ed., Princeton University Press, 1970.Google Scholar