Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
COUPLING FINITE ELEMENTS AND PROPER GENERALIZED DECOMPOSITIONS
RÉSUMÉ
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.
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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
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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
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Ammar, A., Normandin, M., Daim, F., Gonzalez, D., Cueto, E., and Chinesta F., Non-incremental strategies based on separated representations: Applications in computational rheology.
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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
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Bungartz, H. J. and Griebel, M., Sparse grids.
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Cancès, E., Defranceschi, M., Kutzelnigg, W., Le Bris, C., and Maday, Y., Computational Quantum Chemistry: A Primer.
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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
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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
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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
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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
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Gonzalez, D., Ammar, A., Chinesta, F., and Cueto, E., Recent advances in the use of separated representations. DOI: 10.1002/nme.2710
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Ladeveze, P., Non Linear Computational Structural Mechanics.
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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
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Nouy, A., Recent developments in spectral stochastic methods for the solution of stochastic partial differential equations. DOI: 10.1007/s11831-009-9034-5
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Rank, E. and Krause, R., A multiscale finite element method.
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Sreenath, S. N., Cho, K.-H., andWellstead, P., Modelling the dynamics of signalling pathways. DOI: 10.1042/BSE0450001
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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
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Chinesta Francisco, Ladeveze Pierre, Cueto Elías, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, 18, 4, 2011. Crossref
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Kerfriden P., Goury O., Rabczuk T., Bordas S.P.A., A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 256, 2013. Crossref
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El Halabi F., González D., Chico A., Doblaré M., FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition, Computer Methods in Applied Mechanics and Engineering, 257, 2013. Crossref
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Cueto Elías, Chinesta Francisco, Real time simulation for computational surgery: a review, Advanced Modeling and Simulation in Engineering Sciences, 1, 1, 2014. Crossref
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Corigliano A., Dossi M., Mariani S., Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem, Computer Methods in Applied Mechanics and Engineering, 290, 2015. Crossref
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Quesada C., González D., Alfaro I., Cueto E., Huerta A., Chinesta F., Real-time simulation techniques for augmented learning in science and engineering, The Visual Computer, 32, 11, 2016. Crossref
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Canales Diego, Leygue Adrien, Chinesta Francisco, González David, Cueto Elías, Feulvarch Eric, Bergheau Jean-Michel, Huerta Antonio, Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems, International Journal for Numerical Methods in Engineering, 108, 9, 2016. Crossref
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Chinesta Francisco, Huerta Antonio, Rozza Gianluigi, Willcox Karen, Model Reduction Methods, in Encyclopedia of Computational Mechanics Second Edition, 2017. Crossref
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García-Blanco Raquel, Díez Pedro, Borzacchiello Domenico, Chinesta Francisco, Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems, Archives of Computational Methods in Engineering, 25, 4, 2018. Crossref
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Senecal Jaron P., Ji Wei, Characterization of the proper generalized decomposition method for fixed-source diffusion problems, Annals of Nuclear Energy, 126, 2019. Crossref
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Fauque J., Ramière I., Ryckelynck D., Hybrid hyper-reduced modeling for contact mechanics problems, International Journal for Numerical Methods in Engineering, 115, 1, 2018. Crossref
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Chinesta Francisco, Cueto Elías, Introduction, in PGD-Based Modeling of Materials, Structures and Processes, 2014. Crossref
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Chinesta Francisco, Cueto Elías, Space Separation, in PGD-Based Modeling of Materials, Structures and Processes, 2014. Crossref
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Ibáñez Rubén, Abisset‐Chavanne Emmanuelle, Chinesta Francisco, Huerta Antonio, Cueto Elías, A local multiple proper generalized decomposition based on the partition of unity, International Journal for Numerical Methods in Engineering, 120, 2, 2019. Crossref
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Chinesta Francisco, Keunings Roland, Leygue Adrien, Introduction, in The Proper Generalized Decomposition for Advanced Numerical Simulations, 2014. Crossref
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Leon Angel, Mueller Sebastien, de Luca Patrick, Said Rajab, Duval Jean-Louis, Chinesta Francisco, Non-intrusive proper generalized decomposition involving space and parameters: application to the mechanical modeling of 3D woven fabrics, Advanced Modeling and Simulation in Engineering Sciences, 6, 1, 2019. Crossref
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Zhu Liangchao, Li Ming, Martin Ralph R., Direct simulation for CAD models undergoing parametric modifications, Computer-Aided Design, 78, 2016. Crossref