Space\u2013time POD based computational vademecums for parametric studies: application to thermo-mechanical problems

Y Lu,A Gravouil,N Blal

doi:10.1186/s40323-018-0095-6

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.

Highlights

Despite the increasing computer efficiency over the last decades, numerical simulations of welding processes remain prohibitive in terms of CPU time and storage, due to their multi-parametric aspect
This paper proposes a methodology, based on a localized “multi-grid” approach, allowing a quasi-optimal computational vademecum, that provides reliable solutions
Quasi-optimal space–time computational vademecum dedicated to parametric studies of welding process is constructed with a non-intrusive strategy

Summary

Introduction

Despite the increasing computer efficiency over the last decades, numerical simulations of welding processes remain prohibitive in terms of CPU time and storage, due to their multi-parametric aspect. The construction of computational vademecums [1] In Eng. Sci.(2018)5:3 tual charts [2,3] or meta-model computations) with standard computations remains a cumbersome task. The idea of computational vademecums consists in computing at the offline stage general solutions of a parametric problem, so as to make available a database of solutions. The offline computation can be costly, it is advantageous to lose time at this stage compared to that earned at online phase, especially in the case of repetitive tasks. This paper focuses on the construction of numerical vademecums and the reduction of the associated costs for a given level of accuracy

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