ISSN Print: 1543-1649
ISSN Online: 1940-4352
Volume 16, 2018
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Volume 1, 2003
International Journal for Multiscale Computational Engineering
COUPLING FINITE ELEMENTS AND PROPER GENERALIZED DECOMPOSITIONS
Arts et Metiers Paris Tech 2 Boulevard du Ronceray, BP 93525, F-49035 Angers Cedex 01, France
EADS Corporate Foundation International Chair, GeM: UMR CNRS-Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes Cedex 3, France
Group of Structural Mechanics and Materials Modelling (GEMM), Aragon Institute of Engineering Research (I3A), Betancourt Building, Maria de Luna, 5, E-50018 Zaragoza, Spain
Numerous models encountered in science and engineering exist, despite the impressive recent progresses attained in computational simulation techniques, intractable when the usual and experienced discretization techniques are applied for their numerical simulation. Thus, different challenging issues remain for the proposal of new alternative advanced simulation techniques. Separated representations offer the possibility to address some challenging models with CPU time savings of some orders of magnitude. In other cases, they allowed models to be addressed which until now, have never been solved. The number of published works concerning this kind of approximation remains quite reduced, and then numerous difficulties that were successfully circumvented in the context of more experienced discretization techniques, as is the case of the finite element method, must be considered again within the separated representation framework. One of these issues in the one that concerns the treatment of localized behavior of model solutions. This work focuses on this topic and proposes an efficient finite element (or extended finite element) enrichment of usual separated representation.
Ammar, A., Mokdad, B., Chinesta, F., and Keunings, R., A new family of solvers for some clases of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. DOI: 10.1016/j.jnnfm.2006.07.007
Ammar, A., Mokdad, B., Chinesta, F., and Keunings, R., A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Part II: Transient simulation using space-time separated representation. DOI: 10.1016/j.jnnfm.2007.03.009
Ammar, A., Normandin, M., Daim, F., Gonzalez, D., Cueto, E., and Chinesta F., Non-incremental strategies based on separated representations: Applications in computational rheology.
Ammar, A., Chinesta, F., and Falco, A., On the convergence of a greedy rank-one update algorithm for a class of linear systems. DOI: 10.1007/s11831-010-9048-z
Bungartz, H. J. and Griebel, M., Sparse grids.
Cancès, E., Defranceschi, M., Kutzelnigg, W., Le Bris, C., and Maday, Y., Computational Quantum Chemistry: A Primer.
Chinesta, F., Ammar, A., Falco, A., and Laso, M., On the reduction of stochastic kinetic theory models of complex fluids. DOI: 10.1088/0965-0393/15/6/004
Chinesta, F., Ammar, A., and Joyot, P., The nanometric and micrometric scales of the structure and mechanics of materials revisited: An introduction to the challenges of fully deterministic numerical descriptions. DOI: 10.1615/IntJMultCompEng.v6.i3.20
Chinesta, F., Ammar, A., Lemarchand, F., Beauchene, P., and Boust, F., Alleviating mesh constraints: Model reduction, parallel time integration and high resolution homogenization. DOI: 10.1016/j.cma.2007.07.022
Fish, J. and Guttal, R., The s-version of the finite element method for laminated composites. DOI: 10.1002/(SICI)1097-0207(19961115)39:21<3641::AID-NME17>3.0.CO;2-P
Gonzalez, D., Ammar, A., Chinesta, F., and Cueto, E., Recent advances in the use of separated representations. DOI: 10.1002/nme.2710
Ladeveze, P., Non Linear Computational Structural Mechanics.
Ladeveze, P., Passieux, J. Ch., and Neron, D., The LATIN multiscale computational method and the proper orthogonal decomposition. DOI: 10.1016/j.cma.2009.06.023
Nouy, A., Recent developments in spectral stochastic methods for the solution of stochastic partial differential equations. DOI: 10.1007/s11831-009-9034-5
Rank, E. and Krause, R., A multiscale finite element method.
Sreenath, S. N., Cho, K.-H., andWellstead, P., Modelling the dynamics of signalling pathways. DOI: 10.1042/BSE0450001
Sukumar, N., Chopp, D., Moes, N., and Belytschko, T., Modeling holes and inclusions by level sets in the extended finite element method. DOI: 10.1016/S0045-7825(01)00215-8