New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations
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New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations
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Author : Jacques Tagoudjeu
language : en
Publisher: Universal-Publishers
Release Date : 2011-04
New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04 with Mathematics categories.
This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.
New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations
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Author :
language : en
Publisher:
Release Date : 2011
New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1976
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Nuclear energy categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Nbs Special Publication
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Author :
language : en
Publisher:
Release Date : 1965
Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Weights and measures categories.
Computer Literature Bibliography
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1965
Computer Literature Bibliography written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Computers categories.
National Bureau Of Standards Miscellaneous Publication
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Author :
language : en
Publisher:
Release Date : 1965
National Bureau Of Standards Miscellaneous Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Weights and measures categories.
Miscellaneous Publication National Bureau Of Standards
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1965
Miscellaneous Publication National Bureau Of Standards written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Weights and measures categories.
Computer Literature Bibliography 1946 1963
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Author : W. W. Youden
language : en
Publisher:
Release Date : 1965
Computer Literature Bibliography 1946 1963 written by W. W. Youden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Computer science categories.
Energy Research Abstracts
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Author :
language : en
Publisher:
Release Date : 1995
Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Power resources categories.