SCALABLE LINEAR SOLVERS FOR GEOMECHANICS<\/p>\n
Context<\/strong><\/em> Goals<\/strong><\/em> The internship shall result in a PhD of 3 years with EDF R&D.<\/p>\n Required Educational Background<\/strong><\/em><\/p>\n Practicalities<\/strong><\/em><\/p>\n References<\/strong><\/em> Offre de stage<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" SCALABLE LINEAR SOLVERS FOR GEOMECHANICS Context The Electrotechnics and Mechanics Department of EDF R&D has been developing computational software for mechanical and electrotechnical researches for more than twenty years. Its … Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[33],"tags":[],"class_list":["post-2172","post","type-post","status-publish","format-standard","hentry","category-offres-de-these"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"_links":{"self":[{"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/posts\/2172","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/comments?post=2172"}],"version-history":[{"count":1,"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/posts\/2172\/revisions"}],"predecessor-version":[{"id":4315,"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/posts\/2172\/revisions\/4315"}],"wp:attachment":[{"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/media?parent=2172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/categories?post=2172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/csma.fr\/en\/wp-json\/wp\/v2\/tags?post=2172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nThe Electrotechnics and Mechanics Department of EDF R&D has been developing computational software for mechanical and electrotechnical researches for more than twenty years. Its most impacted software, code_aster, is an open source finite element solver and is distributed within the Salome_Meca platform (www.code-aster.org<\/a>).
\nThe background of the internship is the modeling of thermo-hydro-mechanical problems (THM), which describe the behavior of a soil, represented as a porous medium within which evolves a weakly compressible fluid. This is the Biot\u2019s consolidation problem or poro-elasticity problem [1, 2]. This framework is used for instance for studying dams in their environment and the storage of nuclear wastes in the underground.<\/p>\n
\nImportant work has been done on iterative solvers for structural mechanics over the past years. The ability of multigrid methods to solve in a scalable manner standard mechanical problems (not involving Lagrange multipliers i.e. resulting in symmetric positive definite systems) was notably highlighted [3]. However, in the case of the Biot\u2019s problem, the linear systems to be solved are not definite positive.
\nPreliminary work has been carried out in EDF R&D on a simplified version of these equations, involving mechanics of solids, hydraulics and thermics. The method developed in code_aster intensely exploits a
\nmultigrid algorithm in a block preconditioning algorithm. Numerical results on a model problem and more realistic problems reflect the good performance of the proposed preconditioner.
\nThe main goal of the internship consists in extending the approach to the use of a regularization technique which is often mandatory to gain robustness, while introducing new degrees of freedom [4]. The efficiency of the method will be evaluated
\non large scale industrial problems.<\/p>\n\n
\n
\nnicolas.tardieu@edf.fr<\/a> \/ +33 1 78 19 37 49
\nEDF Lab Clamart \/ D\u00e9partement ERMES
\n7 Boulevard Gaspard Monge, 91120 Palaiseau<\/li>\n<\/ul>\n
\n[1] General Theory of Three-Dimensional Consolidation – Maurice Biot, Journal of Applied Physics, 12(2), Pages 155-164, February 1941
\n[2] Poromechanics – Olivier Coussy, Wiley, 2004
\n[3] Multigrid Methods – Stephen F. McCormick, Society for Industrial and Applied Mathematics, January 1987
\n[4] A simplified second gradient model for dilatant materials: Theory and numerical implementation – Rom\u00e9o Fernandes, Cl\u00e9ment Chavant, Ren\u00e9 Chambon, International Journal of Solids and Structures, Volume 45, Issue 20, 1 October 2008, Pages 5289-5307<\/p>\n