Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature, we present a procedure based on a selection of relevant approximations of the eigenspaces for extracting, selecting and reusing information from the Krylov subspaces generated by previous solutions in order to accelerate the current iteration. Assessments of the method are proposed in the cases of both linear and nonlinear structural problems.Comment: International Journal for Numerical Methods in Engineering (2013) 24 page

Substructured formulations of nonlinear structure problems - influence of the interface condition

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a framework where we can swap Newton and DD, so that we solve independent nonlinear problems for each substructure and linear condensed interface problems. The objective is to decrease the number of communications between subdomains and to improve parallelism. Depending on the interface condition, we derive several formulations which are not equivalent, contrarily to the linear case. Primal, dual and mixed variants are described and assessed on a simple plasticity problem.Comment: in International Journal for Numerical Methods in Engineering, Wiley, 201

Multiscale analysis of structures using overlapping nonlinear patches

International audienceWe present here a computational strategy based on overlapping domain decomposition methods. The decomposition is introduced via a partition of the unity applied to the energy. The coupling conditions are imposed via an Augmented Lagrangian on the Sobolev space H1. The nonlinear problem is then condensed on the interface using a nonlinear Schur complement and the interface problem is solved by a Newton-Raphson method

Nonoverlapping domain decomposition for nonlinear elasticity problems: DD with nonlinear localisation

18th International Conference on Domain Decomposition MethodsInternational audienceno abstrac

Extraction et exploitation de modèles réduits dans les solveurs de Krylov

National audienceNous nous intéressons à la résolution d'une succession de problèmes linéaires définis positifs symétriques (à matrices non constantes) par un gradient conjugué. Nous montrons comment il est possible de déduire à faible coût puis d'automatiquement enrichir à l'issue de chaque résolution un modèle réduit dont l'utilisation permet de diminuer fortement le nombre d'itérations à venir

Décomposition de domaine avec localisation non linéaire et partitionnement de modèles

International audienceno abstrac

Computational strategy on nonlinear patches with mixed transfer conditions

USNCCM 9 - 9th US National Congress on Computational MechanicsInternational audienceno abstrac

A nonlinear dual domain decomposition method : application to structural problems with damage

International audienceA dual domain decomposition method dedicated to nonlinear problems is presented. The decomposition is introduced in the nonlinear formulation and the nonlinear problem is first condensed on the interface then solved by a Newton-type method. Considering the specificities of the introduced operators, the algorithm can be interpreted as a local/global strategy with global Newton-type iterations and nonlinear relocalizations per subdomain. Such a strategy is particularly interesting in cases where the nonlinearity is localized. First results are presented on structural problems with damage