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Efficient explicit time stepping for the eXtended Finite Element Method (X‐FEM)
Author(s) -
Menouillard T.,
Réthoré J.,
Combescure A.,
Bung H.
Publication year - 2006
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.1718
Subject(s) - finite element method , discontinuity (linguistics) , mass matrix , element (criminal law) , degrees of freedom (physics and chemistry) , stability (learning theory) , matrix (chemical analysis) , time stepping , order (exchange) , mathematics , computer science , mathematical analysis , structural engineering , physics , engineering , materials science , composite material , finance , machine learning , neutrino , political science , nuclear physics , law , economics , quantum mechanics
This paper focuses on the introduction of a lumped mass matrix for enriched elements, which enables one to use a pure explicit formulation in X‐FEM applications. A proof of stability for the 1D and 2D cases is given. We show that if one uses this technique, the critical time step does not tend to zero as the support of the discontinuity reaches the boundaries of the elements. We also show that the X‐FEM element's critical time step is of the same order as that of the corresponding element without extended degrees of freedom. Copyright © 2006 John Wiley & Sons, Ltd.