Virtual charts of solutions for parametrized nonlinear equations
Résumé
During many decades, engineers relied on experimental abaci to design and optimize mechanical structures. Virtual charts are based on numerical computations and aim at making the design and optimization of structures faster and cheaper as it requires less (or no) experimentation. The parametric problems are solved offline and the associated charts are used for online design. However, in this context, the cost associated to the resolution of parametric problems can be extremely prohibitive. Model reduction techniques are an answer to circumvent this issue. This paper provides the developments of an algorithm for solving nonlinear para-metric problems, based on the LATIN method for the treatment of the nonlinear aspects and the PGD for the parameter dependency. A full time–space-parameter decomposition of the solution is introduced into the LATIN algorithm, numerical examples on academic problems are given so as to point out the advantages of this extension and leads on possible improvements to the strategy are given.