A rational strategy for the resolution of parametrized problems in the PGD framework

This paper deals with the recurring question of the resolution of a problem for many different configurations, which can lead to highly expensive computations when using a direct treatment. The technique which is presented here is based on the use of Proper Generalized Decomposition (PGD) in the framework of the LATIN method. In our previous works, the feasibility of this model reduction technique approach has been demonstrated to compute the solution of a parametrized problem for a given space of parameters. For that purpose, a Reduced-Order Basis (ROB) was 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, inspired by the Reduced Basis method, to explore rationally the space of parameters. The objective is to build, with the minimum of resolutions, a "complete" ROB that enables to solve all the other problems without enriching the basis. We first exemplify the existence of a such complete basis by extracting the most relevant information from the PGD solutions of the problem for all the sets in the space of parameters. Secondly, we propose a rational strategy to build this complete basis without preliminary solving the problem for all the sets of parameters. Finally, the capabilities of the proposed method are illustrated through a variety of examples, showing substantial gains when recurrent studies need to be carried out. (C) 2013 Elsevier B.V. All rights reserved.