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

Mathematical Modelling of Natural Phenomena (2010)

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

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topAwono, 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

top- 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
- 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
- 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. Zbl0601.65017
- D. M. Young. Iterative solution of large linear systems. Academic Press, New York and London, 1971. Zbl0231.65034

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