Julien Pebrel

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.

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

Summary nWe 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 that are not equivalent, contrarily to the linear case. Primal, dual and mixed variants are described and assessed on a simple plasticity problem. Copyright

A computational strategy for contact simulation

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.