Discontinuous Galerkin method; elliptic equation; explicit time integration
Abstract :
[en] An explicit-dynamics spatially-discontinuous Galerkin (DG) formulation for non-linear solid dynamics is proposed and implemented for parallel computation. Discontinuous Galerkin methods have particular appeal in problems involving complex material response, e.g. non-local behavior and failure, as, even in the presence of discontinuities, they provide a rigorous means of ensuring both consistency and stability. In the proposed method, these are guaranteed: the former by the use of average numerical fluxes, and the latter by the introduction of appropriate quadratic terms in the weak formulation. The semi-discrete system of ordinary differential equations is integrated in time using a conventional second-order central-difference explicit scheme. A stability criterion for the time integration algorithm, accounting for the influence of the DG discretization stability, is derived for the equivalent linearized system. This approach naturally lends itself to efficient parallel implementation. The resulting DG computational framework is implemented in three dimensions via specialized interface elements. The versatility, robustness and scalability of the overall computational approach are all demonstrated in problems involving stress-wave propagation and large plastic deformations.
Disciplines :
Mechanical engineering
Author, co-author :
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique
Radovitzky, Raúl; Massachusetts Institute of Technology - MIT > Aeronautics & Astronautics
Language :
English
Title :
An explicit discontinuous Galerkin method for non-linear solid dynamics. Formulation, parallel implementation and scalability properties.
Publication date :
2008
Journal title :
International Journal for Numerical Methods in Engineering
ISSN :
0029-5981
eISSN :
1097-0207
Publisher :
John Wiley & Sons, Inc, Chichester, United Kingdom
F.R.S.-FNRS - Fonds de la Recherche Scientifique This research was supported by the U.S. Army through the Institute for Soldier Nanotechnologies, under Contract DAAD-19-02-D-0002 with the U.S. Army Research Office.
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