Vademecum-based GFEM (V-GFEM): Optimal Enrichment for transient problems

Author (s): Canales, D., Leygue, A., Chinesta, F., González, D., Cueto, E., Feulvarch, E., Bergheau, J.M., and Huerta, A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 108, Issue 9
Pages: 971 – 989
Date: 2016

Abstract:
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 (FEM) 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 (PGD).
Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics which depend on many parameters, such as welding. After introducing the V-GFEM formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.

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Bibtex:

@article {PC-CLCGEFBH:16,
        Author = {Diego Canales and Adrien Leygue and Francisco Chinesta and David Gonz\'alez and El\'{\i}as Cueto and Eric Feulvarch and Jean-Michel Bergheau and Antonio Huerta},
        Title = {\emph{Vademecum}-based GFEM (V-GFEM): Optimal Enrichment for transient problems},
        Fjournal = {International Journal for Numerical Methods in Engineering},
        Journal = {Int. J. Numer. Methods Eng.},
        Volume = {108},
        Number = {9},
        Pages = {971-989},
        Year = {2016},
        Doi = {10.1002/nme.5240}
        }