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Méthodes de décomposition de domaine pour la formulation mixte duale du problème critique de la diffusion des neutrons

Pierre Guérin 1
1 LLPR - Laboratoire de Logiciels pour la Physique des Réacteurs
SERMA - Service des Réacteurs et de Mathématiques Appliquées : DEN/DM2S/SERMA
Abstract : The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping subdomains. Several eigenmodes solutions of a local problem solved by MINOS on each subdomain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each subdomain by MINOS with the interface conditions deduced from the solutions on the adjacent subdomains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2D and 3D cores.
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Submitted on : Monday, January 21, 2008 - 10:33:34 AM
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Pierre Guérin. Méthodes de décomposition de domaine pour la formulation mixte duale du problème critique de la diffusion des neutrons. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00210588⟩

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