Abstract
In this paper, we analyse the convergence of the inner-outer iteration scheme for determining the multiplication factor and the fundamental mode neutron distribution within the finite differenced approximation to the multi-group neutron diffusion equation. We show that a set of four sufficient conditions, on the number of inner iterations to be performed, can be obtained which would guarantee the convergence of the scheme. A few special cases are analysed where we determine the minimum number of inner iterations required for convergence.
Zusammenfassung
Gegenstand der Arbeit ist die Konvergenz des „inner-outer“ Iterationsschemas zur Berechnung des Multiplikationsfaktors und der Grundverteilung der Neutronen in der Differenzenapproximation zur eingruppigen Neutronendiffusionsgleichung. Wir erhalten vier Bedingungen für die Anzahl der auszuführenden äußeren Iterationen, die zur Erzielung der Konvergenz hinreichen. In einigen Spezialfällen bestimmen wir auch die Minimalzahl der für die Konvergenz erforderlichen inneren Iterationen.
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References
L. A. Hageman,Numerical methods and techniques used in the two dimensional diffusion program PDQ-5, WAPD-TM-364 (1963). L. A. Hageman and C. J. Pfeifer, Utilization of the neutron diffusion program PDQ-5, WAPD-TM-395 (1965). Also see L. A. Hageman, The estimation of acceleration parameters WAPD-TM-1038 (1972).
E. L. Wachspress,Iterative solution of elliptic systems and applications to the neutron diffusion equations of reactor physics. Prentice-Hall, Englewood Cliffs, N. J., (1966).
D. R. Ferguson and K. L. Derstine, N. S. E.,64, (1977).
R. S. Varga, Proc. Symp. in applied mathematics, A. M. S.,11, 164 (1961).
R. S. Varga,Matrix iterative analysis. Prentice-Hall International, London 1962.
N. K. Nichols, S.I.A.M. J. Numer. Anal.10, 460 (1973).
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Menon, S.V.G., Khandekar, D.C. Convergence of the inner-outer iteration scheme. Z. angew. Math. Phys. 35, 321–331 (1984). https://doi.org/10.1007/BF00944881
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DOI: https://doi.org/10.1007/BF00944881