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

Thumbnail Image

Files

s40323-018-0095-6.pdf (2.51 MB)

Links to Files

https://link.springer.com/article/10.1186/s40323-018-0095-6

Permanent Link

https://doi.org/10.1186/s40323-018-0095-6
 http://hdl.handle.net/11603/30032

Collections

UMBC Mechanical Engineering Department

Author/Creator

Author/Creator ORCID

https://orcid.org/0000-0003-3698-5596

Date

2018-02-13

Type of Work

journal articles
Text

Department

Program

Citation of Original Publication

Lu, Y., Blal, N. & Gravouil, A. Space–time POD based computational vademecums for parametric studies: application to thermo-mechanical problems. Adv. Model. and Simul. in Eng. Sci. 5, 3 (2018). https://doi.org/10.1186/s40323-018-0095-6

Rights

This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Attribution 4.0 International (CC BY 4.0)

Subjects

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.