Time‐space PGD for the rapid solution of 3D nonlinear parametrized problems in the many‐query context

Summary This work deals with the question of the resolution of nonlinear problems for many different configurations in order to build a ‘virtual chart’ of solutions. The targeted problems are three‐dimensional structures driven by Chaboche‐type elastic‐viscoplastic constitutive laws. In this context, parametric analysis can lead to highly expensive computations when using a direct treatment. As an alternative, we present a technique based on the use of the time‐space proper generalized decomposition in the framework of the LATIN method. To speed up the calculations in the parametrized context, we use the fact that at each iteration of the LATIN method, an approximation over the entire time‐space domain is available. Then, a global reduced‐order basis is generated, reused and eventually enriched, by treating, one‐by‐one, all the various parameter sets. The novelty of the current paper is to develop a strategy that uses the reduced‐order basis for any new set of parameters as an initialization for the iterative procedure. The reduced‐order basis, which has been built for a set of parameters, is reused to build a first approximation of the solution for another set of parameters. An error indicator allows adding new functions to the basis only if necessary. The gain of this strategy for studying the influence of material or loading variability reaches the order of 25 in the industrial examples that are presented. Copyright © 2015 John Wiley & Sons, Ltd.