Space–time POD based computational vademecums for parametric studies: application to thermo-mechanical problems

Abstract

Abstract Standard numerical simulations for optimization or inverse identification of welding processes remain costly and difficult due to their multi-parametric aspect and inherent complexity. The aim of this paper is to propose a non-intrusive strategy for building computational vademecums dedicated to real-time simulations of nonlinear thermo-mechanical problems. There is in essence, a set of precomputed space–time parametric solutions (snapshots), selected by an appropriate approach in the parameter space and stored in memory as quasi-optimal reduced bases (RBs) provided by the proper orthogonal decomposition method. Once the RBs are obtained, the computational vademecums can be used online and provide real-time space–time transient nonlinear thermo-mechanical solutions for any desired parameter value. The contributions of the paper consist in a space–time RBs interpolation approach with the Grassmann manifolds method, and a localized multigrid selection method that allows an automatic selection of snapshots in the parameter areas of interest for a given level of accuracy. As application, the welding simulation is considered with a transient non-linear thermo-mechanical model using the finite element method. It is shown that the moving frame allows an optimal design of the RBs. A good efficiency of the proposed approach is demonstrated. Computational vademecums can be used for optimization or inverse identification problems of welding.

Keywords

• Computational vademecums
• POD
• localized multigrid selection
• Grassmann manifold interpolation