We study the implementation of a domain decomposition method for structures with quasi-incompress... more We study the implementation of a domain decomposition method for structures with quasi-incompressible components. We chose a mixed formulation where the pressure field is discontinuous on the interfaces between substructures. We propose an extension of classical preconditioners to this class of problems. The numerical simulation of the mechanical behaviour of the flexible bearing of the nozzle of a solid propellant booster is then conducted using various Newton-Krylov parallel approaches. We present the main mechanical results and compare the numerical performance of the parallel approaches to a sequential approach. RÉSUMÉ. Nous étudions la mise en oeuvre d'une méthode de décomposition de domaine pour structures à composants quasi-incompressibles. Une formulation mixte à champ de pression discontinu aux interfaces entre sous-structures est retenue ; nous proposons, pour cette classe de problèmes, une extension des préconditionneurs classiques. La mise en oeuvre de la simulation numérique du comportement mécanique d'une butée flexible de tuyère de propulseur à propergol solide par diverses approches parallèles itératives de type Newton-Krylov est alors proposée. Nous présentons les principaux résultats mécaniques ainsi que les performances numériques obtenues par les approches parallèles retenues et une approche séquentielle. KEYWORDS: Domain decomposition method, Newton-Krylov, quasi incompressibility, mixed formulation MOTS-CLÉS : Méthode de décomposition de domaine, Newton-Krylov, quasi incompressibilité, formulation mixte -0 /2002. , pages 1 à 15
Proceedings of the Sixth International Conference on Engineering Computational Technology, 2008
In this presentation we consider efficient numerical strategies designed to compute the evolution... more In this presentation we consider efficient numerical strategies designed to compute the evolution of large structures undergoing localized nonlinear phenomena such as plasticity, damage, cracking or microbuckling. Despite Newton-Schur-Krylov strategies which associate both Newton type solvers and domain decomposition methods (and especially non-overlapping ones [1,2]) provide an efficient framework for the solution to large systems, in the case of localized nonlinearity the global convergence of the problem may be penalized, leading to the solution to many global systems. Moreover localized nonlinearities often come with other difficulties such as the necessity to adapt the mesh and the time stepping.
La résolution de problèmes de délaminage dans les structures stratifiées de grande taille, modéli... more La résolution de problèmes de délaminage dans les structures stratifiées de grande taille, modélisées à l'échelle mésoscopique, nécessite l'emploi de méthodes parallèles. La stratégie à la base de nos travaux est un solveur itératif de problèmes non-linéaires sous-structurés, incluant une phase de résolution d'un problème homogénéisé global nécessaire à l'obtention de l'extensibilité numérique. Cet article propose une résolution efficace de ce problème dans le cas du délaminage de grandes structures, traité ici par utilisation d'interfaces cohésives.
Lecture Notes in Computational Science and Engineering, 2007
Domain decomposition solvers are popular for engineering analysis of applications such as car bod... more Domain decomposition solvers are popular for engineering analysis of applications such as car bodies, tires, oil reservoirs, or aerospace structures. These methods have shown to be very efficient in exploiting high performance computing capabilities. Nevertheless a significant gap remains between their optimality as predicted from idealized mathematical analysis and the lack of robustness experienced in many applications.
Une comparaison entre trois approches de décomposition de domaine (DDM) dédiées aux problèmes non... more Une comparaison entre trois approches de décomposition de domaine (DDM) dédiées aux problèmes non-linéaires est présentée. Basées sur la condensation du problème non linéaire, ces stratégies mènent à la résolution d'un problème tangent d'interface et de problèmes locaux non linéaires. Le problème d'interface rentre dans le cadre usuel des DDM linéaires (FETI, BDD, etc) ; les problèmes locaux non-linéaires peuvent être résolus avec différents types de conditions aux limites (Dirichlet, Neumann, Robin), dont le rôle est évalué dans cette étude.
This paper presents a computational strategy for structural problems that exhibit nonlinear pheno... more This paper presents a computational strategy for structural problems that exhibit nonlinear phenomena in a small critical zone while the rest of the structure retains a linear elastic behavior. The method uses two finite element models: a global linear elastic model that represents the whole structure, and a local elastic-plastic "submodel" meant to replace the global model in the critical zone. This replacement is performed in an exact manner using a non-intrusive coupling technique, which never modifies the existing model data and uses standard finite element software to carry out the computations. Several variants are presented and applied on 2D and 3D examples.
III European Conference on Computational Mechanics, 2006
We consider the simulation of structures undergoing frictional contact conditions. The chosen for... more We consider the simulation of structures undergoing frictional contact conditions. The chosen formulation [1] coupled with a Newton-like solver, leads to the resolution of a sequence of non-symmetric linear systems with non-invariant matrices. We propose a computational strategy based on non-overlapping domain decomposition method [2], 3, [4] and augmented Krylov iterative solvers [5]. After each Newton iteration, numerical information on the condensed interface problem is stored inside so called Krylov subspace; we propose to reinject most significant part of this information inside a second scale problem in order to accelerate the resolution of following systems. This strategy can be viewed as an extension of previous works [6] to non-symmetric problems: new strategies to build reused information and relevance estimators are assessed.
Computer Methods in Applied Mechanics and Engineering, 2015
This paper deals with bounding the error on the estimation of quantities of interest obtained by ... more This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution of reference and adjoint problems : on the one hand the discretization error due to the finite element method and on the other hand the algebraic error due to the use of the iterative solver. Beside practical considerations on the parallel computation of the bounds, it is shown that the interface conformity can be slightly relaxed so that local enrichment or refinement are possible in the subdomains bearing singularities or quantities of interest which simplifies the improvement of the estimation. Academic assessments are given on 2D static linear mechanic problems.
We study the implementation of a domain decomposition method for structures with quasi-incompress... more We study the implementation of a domain decomposition method for structures with quasi-incompressible components. We chose a mixed formulation where the pressure field is discontinuous on the interfaces between substructures. We propose an extension of classical preconditioners to this class of problems. The numerical simulation of the mechanical behaviour of the flexible bearing of the nozzle of a solid propellant booster is then conducted using various Newton-Krylov parallel approaches. We present the main mechanical results and compare the numerical performance of the parallel approaches to a sequential approach. RÉSUMÉ. Nous étudions la mise en oeuvre d'une méthode de décomposition de domaine pour structures à composants quasi-incompressibles. Une formulation mixte à champ de pression discontinu aux interfaces entre sous-structures est retenue ; nous proposons, pour cette classe de problèmes, une extension des préconditionneurs classiques. La mise en oeuvre de la simulation numérique du comportement mécanique d'une butée flexible de tuyère de propulseur à propergol solide par diverses approches parallèles itératives de type Newton-Krylov est alors proposée. Nous présentons les principaux résultats mécaniques ainsi que les performances numériques obtenues par les approches parallèles retenues et une approche séquentielle. KEYWORDS: Domain decomposition method, Newton-Krylov, quasi incompressibility, mixed formulation MOTS-CLÉS : Méthode de décomposition de domaine, Newton-Krylov, quasi incompressibilité, formulation mixte -0 /2002. , pages 1 à 15
Proceedings of the Sixth International Conference on Engineering Computational Technology, 2008
In this presentation we consider efficient numerical strategies designed to compute the evolution... more In this presentation we consider efficient numerical strategies designed to compute the evolution of large structures undergoing localized nonlinear phenomena such as plasticity, damage, cracking or microbuckling. Despite Newton-Schur-Krylov strategies which associate both Newton type solvers and domain decomposition methods (and especially non-overlapping ones [1,2]) provide an efficient framework for the solution to large systems, in the case of localized nonlinearity the global convergence of the problem may be penalized, leading to the solution to many global systems. Moreover localized nonlinearities often come with other difficulties such as the necessity to adapt the mesh and the time stepping.
La résolution de problèmes de délaminage dans les structures stratifiées de grande taille, modéli... more La résolution de problèmes de délaminage dans les structures stratifiées de grande taille, modélisées à l'échelle mésoscopique, nécessite l'emploi de méthodes parallèles. La stratégie à la base de nos travaux est un solveur itératif de problèmes non-linéaires sous-structurés, incluant une phase de résolution d'un problème homogénéisé global nécessaire à l'obtention de l'extensibilité numérique. Cet article propose une résolution efficace de ce problème dans le cas du délaminage de grandes structures, traité ici par utilisation d'interfaces cohésives.
Lecture Notes in Computational Science and Engineering, 2007
Domain decomposition solvers are popular for engineering analysis of applications such as car bod... more Domain decomposition solvers are popular for engineering analysis of applications such as car bodies, tires, oil reservoirs, or aerospace structures. These methods have shown to be very efficient in exploiting high performance computing capabilities. Nevertheless a significant gap remains between their optimality as predicted from idealized mathematical analysis and the lack of robustness experienced in many applications.
Une comparaison entre trois approches de décomposition de domaine (DDM) dédiées aux problèmes non... more Une comparaison entre trois approches de décomposition de domaine (DDM) dédiées aux problèmes non-linéaires est présentée. Basées sur la condensation du problème non linéaire, ces stratégies mènent à la résolution d'un problème tangent d'interface et de problèmes locaux non linéaires. Le problème d'interface rentre dans le cadre usuel des DDM linéaires (FETI, BDD, etc) ; les problèmes locaux non-linéaires peuvent être résolus avec différents types de conditions aux limites (Dirichlet, Neumann, Robin), dont le rôle est évalué dans cette étude.
This paper presents a computational strategy for structural problems that exhibit nonlinear pheno... more This paper presents a computational strategy for structural problems that exhibit nonlinear phenomena in a small critical zone while the rest of the structure retains a linear elastic behavior. The method uses two finite element models: a global linear elastic model that represents the whole structure, and a local elastic-plastic "submodel" meant to replace the global model in the critical zone. This replacement is performed in an exact manner using a non-intrusive coupling technique, which never modifies the existing model data and uses standard finite element software to carry out the computations. Several variants are presented and applied on 2D and 3D examples.
III European Conference on Computational Mechanics, 2006
We consider the simulation of structures undergoing frictional contact conditions. The chosen for... more We consider the simulation of structures undergoing frictional contact conditions. The chosen formulation [1] coupled with a Newton-like solver, leads to the resolution of a sequence of non-symmetric linear systems with non-invariant matrices. We propose a computational strategy based on non-overlapping domain decomposition method [2], 3, [4] and augmented Krylov iterative solvers [5]. After each Newton iteration, numerical information on the condensed interface problem is stored inside so called Krylov subspace; we propose to reinject most significant part of this information inside a second scale problem in order to accelerate the resolution of following systems. This strategy can be viewed as an extension of previous works [6] to non-symmetric problems: new strategies to build reused information and relevance estimators are assessed.
Computer Methods in Applied Mechanics and Engineering, 2015
This paper deals with bounding the error on the estimation of quantities of interest obtained by ... more This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution of reference and adjoint problems : on the one hand the discretization error due to the finite element method and on the other hand the algebraic error due to the use of the iterative solver. Beside practical considerations on the parallel computation of the bounds, it is shown that the interface conformity can be slightly relaxed so that local enrichment or refinement are possible in the subdomains bearing singularities or quantities of interest which simplifies the improvement of the estimation. Academic assessments are given on 2D static linear mechanic problems.
Uploads
Papers by P. Gosselet