A splitting iterative method for solving the neutron transport equation

This paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergenc...

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Main Authors: Onana Awono, Jacques Tagoudjeu
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2009-09-01
Series:Mathematical Modelling and Analysis
Subjects:
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/6548
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author Onana Awono
Jacques Tagoudjeu
author_facet Onana Awono
Jacques Tagoudjeu
author_sort Onana Awono
collection DOAJ
description This paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergence of the method is numerically illustrated and compared with the standard Source Iteration method and multigrid method on sample problems in slab geometry and in two dimensional space. First published online: 14 Oct 2010
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spelling doaj.art-e1476bc422834dd68a44cefced53f73c2022-12-21T20:21:04ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102009-09-0114310.3846/1392-6292.2009.14.271-289A splitting iterative method for solving the neutron transport equationOnana Awono0Jacques Tagoudjeu1Ecole Nationale Supérieure Polytechnique, University of Yaoundé I; Po.Box 8390 Yaoundé, CameroonEcole Nationale Supérieure Polytechnique, University of Yaoundé I; Faculty of Science, University of Yaoundé I; Po.Box 812 Yaoundé, CameroonThis paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergence of the method is numerically illustrated and compared with the standard Source Iteration method and multigrid method on sample problems in slab geometry and in two dimensional space. First published online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/6548Transport equationself adjoint operatorm‐accretiveoperator splittingiterative method
spellingShingle Onana Awono
Jacques Tagoudjeu
A splitting iterative method for solving the neutron transport equation
Mathematical Modelling and Analysis
Transport equation
self adjoint operator
m‐accretive
operator splitting
iterative method
title A splitting iterative method for solving the neutron transport equation
title_full A splitting iterative method for solving the neutron transport equation
title_fullStr A splitting iterative method for solving the neutron transport equation
title_full_unstemmed A splitting iterative method for solving the neutron transport equation
title_short A splitting iterative method for solving the neutron transport equation
title_sort splitting iterative method for solving the neutron transport equation
topic Transport equation
self adjoint operator
m‐accretive
operator splitting
iterative method
url https://journals.vgtu.lt/index.php/MMA/article/view/6548
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