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Vademecum ‐based GFEM (V‐GFEM): optimal enrichment for transient problems
Author(s) -
Canales Diego,
Leygue Adrien,
Chinesta Francisco,
González David,
Cueto Elías,
Feulvarch Eric,
Bergheau JeanMichel,
Huerta Antonio
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5240
Subject(s) - finite element method , parametric statistics , computation , computer science , welding , transient (computer programming) , key (lock) , mathematics , parametric model , mathematical optimization , line (geometry) , algorithm , computational science , structural engineering , mechanical engineering , engineering , geometry , statistics , computer security , operating system
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.