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

O. Awono; J. Tagoudjeu

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 60-66
  • ISSN: 0973-5348

Abstract

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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

How to cite

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Awono, O., and Tagoudjeu, J.. Taik, A., ed. "A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation." Mathematical Modelling of Natural Phenomena 5.7 (2010): 60-66. <http://eudml.org/doc/197695>.

@article{Awono2010,
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},
author = {Awono, O., Tagoudjeu, J.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {neutron transport; operator splitting; self-adjoint; m-accretive; iterative methods; SOR acceleration; minimal residual methods; preconditioning; selfadjoint operator},
language = {eng},
month = {8},
number = {7},
pages = {60-66},
publisher = {EDP Sciences},
title = {A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation},
url = {http://eudml.org/doc/197695},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Awono, O.
AU - Tagoudjeu, J.
AU - Taik, A.
TI - A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 60
EP - 66
AB - 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
LA - eng
KW - neutron transport; operator splitting; self-adjoint; m-accretive; iterative methods; SOR acceleration; minimal residual methods; preconditioning; selfadjoint operator
UR - http://eudml.org/doc/197695
ER -

References

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  1. Awona Onana and J. Tagoudjeu. Iterative methods for a class of linear operator equations. Int. J. Contemp. Math. Sci., 4 (2009), No. 12, 549–564. Zbl1177.65077
  2. O. Awono and J. Tagoudjeu. A splitting iterative method for solving the neutron transport equation. Math. Model. Anal., 14 (2009), No. 3, 271–289. Zbl1180.82243
  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.  Zbl0601.65017
  5. D. M. Young. Iterative solution of large linear systems. Academic Press, New York and London, 1971.  Zbl0231.65034

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