Geodesic
A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
O. Awono1 ; J. Tagoudjeu1, 2
1 ENSP, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon
2 Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 60-66.

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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
DOI : 10.1051/mmnp/201057010

O. Awono 1 ; J. Tagoudjeu 1, 2

1 ENSP, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon
2 Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon 
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O. Awono; J. Tagoudjeu. A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 60-66. doi : 10.1051/mmnp/201057010. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201057010/

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[2] O. Awono, J. Tagoudjeu A splitting iterative method for solving the neutron transport equation Math. Model. Anal. 2009 271 289

[3] 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.

[4] P. Lascaux and R. Théodor. Analyse numérique matricielle appliquée à l’Art de l’Ingénieur. Volume 2, Masson, Paris, 1987.

[5] D. M. Young. Iterative solution of large linear systems. Academic Press, New York and London, 1971.

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