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A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
O. Awono  and
J. Tagoudjeu
O. Awono
Affiliation:
ENSP, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon
J. Tagoudjeu*
Affiliation:
ENSP, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
*
*Corresponding author: E-mail: jtagoudjeu@gmail.com
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Abstract

We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of a SOR algorithm is then applied to solve the matrix operator equation. Theoretical and numerical results of convergence are given

Keywords

neutron transportoperator splittingself-adjointm-accretiveiterative methodsSOR acceleration
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9th International Conference on Numerical Analysis and Optimization , 2010 , pp. 60 - 66
Copyright
© EDP Sciences, 2010

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References

Onana, Awona and Tagoudjeu, J.. Iterative methods for a class of linear operator equations . Int. J. Contemp. Math. Sci., 4 (2009), No. 12, 549–564.Google Scholar
Awono, O. and Tagoudjeu, J.. A splitting iterative method for solving the neutron transport equation . Math. Model. Anal., 14 (2009), No. 3, 271–289.CrossRefGoogle Scholar
O. Awono and J. Tagoudjeu. A self-adjoint and m-accretive splitting iterative method for solving the neutron transport equation in 1-D sphérical geometry. Proceeding of CARI’08 Rabat-Morocco, (2008), 331–338.
P. Lascaux and R. Théodor. Analyse numérique matricielle appliquée à l’Art de l’Ingénieur. Volume 2, Masson, Paris, 1987.
D. M. Young. Iterative solution of large linear systems. Academic Press, New York and London, 1971.