Vademecum‐based GFEM (V‐GFEM): optimal enrichment for transient problems. (10th March 2016)

• Record Type: Journal Article
• Authors: Canales, Diego; Leygue, Adrien; Chinesta, Francisco; González, David; Cueto, Elías; Feulvarch, Eric; Bergheau, Jean‐Michel; Huerta, Antonio
• Is Part Of: International journal for numerical methods in engineering. Volume 108:Number 9(2016)
• Page Start: 971
• Page End: 989
• Publication Date: 2016-03-10
• Subjects: vademecum‐based generalized finite element method -- generalized finite element method -- proper generalized decomposition -- transient problem -- welding simulation; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5240
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.