New splitting iterative methods for solving multidimensional neutron transport equations /:
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. :
Dissertation.com,
2011.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Annotation |
| Beschreibung: | Title from PDF title page (viewed on May 1, 2013). |
| Beschreibung: | 1 online resource : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781612338873 1612338879 |
Internformat
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| 100 | 1 | |a Tagoudjeu, Jacques. | |
| 245 | 1 | 0 | |a New splitting iterative methods for solving multidimensional neutron transport equations / |c Jacques Tagoudjeu. |
| 260 | |a Boca Raton, Fla. : |b Dissertation.com, |c 2011. | ||
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| 520 | 8 | |a Annotation |b This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of R<sup>n</sup> (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. | |
| 650 | 0 | |a Neutron transport theory. |0 http://id.loc.gov/authorities/subjects/sh85091220 | |
| 650 | 0 | |a Nuclear reactors. |0 http://id.loc.gov/authorities/subjects/sh85093071 | |
| 650 | 0 | |a Iterative methods (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85069058 | |
| 650 | 2 | |a Nuclear Reactors |0 https://id.nlm.nih.gov/mesh/D009688 | |
| 650 | 6 | |a Théorie du transport des neutrons. | |
| 650 | 6 | |a Réacteurs nucléaires. | |
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| spelling | Tagoudjeu, Jacques. New splitting iterative methods for solving multidimensional neutron transport equations / Jacques Tagoudjeu. Boca Raton, Fla. : Dissertation.com, 2011. 1 online resource : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references. Title from PDF title page (viewed on May 1, 2013). Annotation This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of R<sup>n</sup> (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. Neutron transport theory. http://id.loc.gov/authorities/subjects/sh85091220 Nuclear reactors. http://id.loc.gov/authorities/subjects/sh85093071 Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Nuclear Reactors https://id.nlm.nih.gov/mesh/D009688 Théorie du transport des neutrons. Réacteurs nucléaires. Itération (Mathématiques) nuclear reactors. aat SCIENCE Physics Nuclear. bisacsh Iterative methods (Mathematics) fast Neutron transport theory fast Nuclear reactors fast FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=538782 Volltext |
| spellingShingle | Tagoudjeu, Jacques New splitting iterative methods for solving multidimensional neutron transport equations / Neutron transport theory. http://id.loc.gov/authorities/subjects/sh85091220 Nuclear reactors. http://id.loc.gov/authorities/subjects/sh85093071 Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Nuclear Reactors https://id.nlm.nih.gov/mesh/D009688 Théorie du transport des neutrons. Réacteurs nucléaires. Itération (Mathématiques) nuclear reactors. aat SCIENCE Physics Nuclear. bisacsh Iterative methods (Mathematics) fast Neutron transport theory fast Nuclear reactors fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85091220 http://id.loc.gov/authorities/subjects/sh85093071 http://id.loc.gov/authorities/subjects/sh85069058 https://id.nlm.nih.gov/mesh/D009688 |
| title | New splitting iterative methods for solving multidimensional neutron transport equations / |
| title_auth | New splitting iterative methods for solving multidimensional neutron transport equations / |
| title_exact_search | New splitting iterative methods for solving multidimensional neutron transport equations / |
| title_full | New splitting iterative methods for solving multidimensional neutron transport equations / Jacques Tagoudjeu. |
| title_fullStr | New splitting iterative methods for solving multidimensional neutron transport equations / Jacques Tagoudjeu. |
| title_full_unstemmed | New splitting iterative methods for solving multidimensional neutron transport equations / Jacques Tagoudjeu. |
| title_short | New splitting iterative methods for solving multidimensional neutron transport equations / |
| title_sort | new splitting iterative methods for solving multidimensional neutron transport equations |
| topic | Neutron transport theory. http://id.loc.gov/authorities/subjects/sh85091220 Nuclear reactors. http://id.loc.gov/authorities/subjects/sh85093071 Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Nuclear Reactors https://id.nlm.nih.gov/mesh/D009688 Théorie du transport des neutrons. Réacteurs nucléaires. Itération (Mathématiques) nuclear reactors. aat SCIENCE Physics Nuclear. bisacsh Iterative methods (Mathematics) fast Neutron transport theory fast Nuclear reactors fast |
| topic_facet | Neutron transport theory. Nuclear reactors. Iterative methods (Mathematics) Nuclear Reactors Théorie du transport des neutrons. Réacteurs nucléaires. Itération (Mathématiques) nuclear reactors. SCIENCE Physics Nuclear. Neutron transport theory Nuclear reactors |
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