Publicou 6 edições por ano
ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352
Indexed in
The Nanometric and Micrometric Scales of the Structure and Mechanics of Materials Revisited: An Introduction to the Challenges of Fully Deterministic Numerical Descriptions
RESUMO
Nanoscience and nanotechnology as well as the fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales use descriptions ranging from the quantum to the statistical mechanics. This article revisits the modeling at these scales and points out the main challenges related to the numerical solution of such models that sometimes are discrete but involve an extremely large number of particles (as is the case of molecular dynamics simulations or coarse-grained molecular dynamics) and other times are continuous but defined in highly multidimensional spaces, leading to the well-known curse of dimensionality issues. The curse of dimensionality of some of these deterministic models will be emphasized, and their numerical implications will be addressed in the second part of this work.
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Chinesta F., Ammar A., Cueto E., Proper generalized decomposition of multiscale models, International Journal for Numerical Methods in Engineering, 83, 8-9, 2010. Crossref
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Bognet B., Bordeu F., Chinesta F., Leygue A., Poitou A., Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity, Computer Methods in Applied Mechanics and Engineering, 201-204, 2012. Crossref
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Alotto P., Guarnieri M., Moro F., Stella A., Multi-physic 3D dynamic modelling of polymer membranes with a proper generalized decomposition model reduction approach, Electrochimica Acta, 57, 2011. Crossref
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Park H.M., Karhunen–Loève Galerkin method with decimated sampling technique for the simulation of complex fluids defined in the phase space, Journal of Non-Newtonian Fluid Mechanics, 165, 19-20, 2010. Crossref
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Bonithon G., Joyot P., Chinesta F., Villon P., Non-incremental boundary element discretization of parabolic models based on the use of the proper generalized decompositions, Engineering Analysis with Boundary Elements, 35, 1, 2011. Crossref
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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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Pruliere E., Chinesta F., Ammar A., On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Mathematics and Computers in Simulation, 81, 4, 2010. Crossref
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Cruz C., Chinesta F., Régnier G., Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology, Archives of Computational Methods in Engineering, 19, 2, 2012. Crossref
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Lamari H., Ammar A., Cartraud P., Legrain G., Chinesta F., Jacquemin F., Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions, Archives of Computational Methods in Engineering, 17, 4, 2010. Crossref
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Chinesta Francisco, Ammar Amine, Cueto Elías, Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models, Archives of Computational Methods in Engineering, 17, 4, 2010. Crossref
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Ammar Amine, Cueto Elías, Chinesta Francisco, Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions, International Journal for Numerical Methods in Biomedical Engineering, 28, 9, 2012. Crossref
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Leygue A., Verron E., A First Step Towards the Use of Proper General Decomposition Method for Structural Optimization, Archives of Computational Methods in Engineering, 17, 4, 2010. Crossref
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Sarbandi B., Cartel S., Besson J., Ryckelynck D., Truncated Integration for Simultaneous Simulation of Sintering Using a Separated Representation, Archives of Computational Methods in Engineering, 17, 4, 2010. Crossref
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Ammar Amine, Chinesta Francisco, Cueto Elías, Doblaré Manuel, Proper generalized decomposition of time-multiscale models, International Journal for Numerical Methods in Engineering, 90, 5, 2012. Crossref
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Dumon A., Allery C., Ammar A., Simulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD), Numerical Heat Transfer, Part B: Fundamentals, 63, 1, 2013. Crossref
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González David, Cueto Elías, Chinesta Francisco, Díez Pedro, Huerta Antonio, Streamline upwind/Petrov-Galerkin-based stabilization of proper generalized decompositions for high-dimensional advection-diffusion equations, International Journal for Numerical Methods in Engineering, 94, 13, 2013. Crossref
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Chinesta Francisco, From Single-Scale to Two-Scales Kinetic Theory Descriptions of Rods Suspensions, Archives of Computational Methods in Engineering, 20, 1, 2013. Crossref
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Chinesta F., Leygue A., Bordeu F., Aguado J. V., Cueto E., Gonzalez D., Alfaro I., Ammar A., Huerta A., PGD-Based Computational Vademecum for Efficient Design, Optimization and Control, Archives of Computational Methods in Engineering, 20, 1, 2013. Crossref
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Leblond C., Allery C., A priori space–time separated representation for the reduced order modeling of low Reynolds number flows, Computer Methods in Applied Mechanics and Engineering, 274, 2014. Crossref
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Alotto P., Guarnieri M., Moro F., Stella A., A Proper Generalized Decomposition Approach for Fuel Cell Polymeric Membrane Modeling, IEEE Transactions on Magnetics, 47, 5, 2011. Crossref
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Lopez Elena, Abisset-Chavanne Emmanuelle, Lebel François, Upadhyay Ram, Comas Sébastien, Binetruy Christophe, Chinesta Francisco, Advanced thermal simulation of processes involving materials exhibiting fine-scale microstructures, International Journal of Material Forming, 9, 2, 2016. Crossref
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Chinesta F., Abisset-Chavanne E., Ammar A., Cueto E., Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations, Communications in Computational Physics, 17, 4, 2015. Crossref
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Alotto P., Guarnieri M., Moro F., Stella A., A proper generalized decomposition approach for modeling fuel cell polymeric membranes, Digests of the 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation, 2010. Crossref
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Ammar Amine, Zghal Ali, Morel Franck, Chinesta Francisco, On the space-time separated representation of integral linear viscoelastic models, Comptes Rendus Mécanique, 343, 4, 2015. Crossref
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Cimetiere Alain, Chinesta Francisco, Visonneau Michel, Leygue Adrien, Xu Guangtao, Ghnatios Chady, On the space separated representation when addressing the solution of PDE in complex domains, Discrete and Continuous Dynamical Systems - Series S, 9, 2, 2016. Crossref
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Chinesta Francisco, Magnin Morgan, Roux Olivier, Ammar Amine, Cueto Elias, Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions, Entropy, 17, 4, 2015. 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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Chinesta Francisco, Abisset-Chavanne Emmanuelle, The Schrödinger Equation, in A Journey Around the Different Scales Involved in the Description of Matter and Complex Systems, 2018. Crossref
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Le-Quoc C., Le Linh A., Ho-Huu V., Huynh P. D., Nguyen-Thoi T., An Immersed Boundary Proper Generalized Decomposition (IB-PGD) for Fluid–Structure Interaction Problems, International Journal of Computational Methods, 15, 06, 2018. Crossref
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Balducci Marc, Jones Brandon, Doostan Alireza, Orbit uncertainty propagation and sensitivity analysis with separated representations, Celestial Mechanics and Dynamical Astronomy, 129, 1-2, 2017. Crossref
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Chinesta Francisco, Ammar Amine, Cueto Elías, On the use of proper generalized decompositions for solving the multidimensional chemical master equation, European Journal of Computational Mechanics, 19, 1-3, 2010. Crossref
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Nasri Mohamed Aziz, Robert Camille, Ammar Amine, El Arem Saber, Morel Franck, Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading, Comptes Rendus Mécanique, 346, 2, 2018. Crossref
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Dumon Antoine, Allery Cyrille, Ammar Amine, Proper Generalized Decomposition method for incompressible flows in stream-vorticity formulation, European Journal of Computational Mechanics, 19, 5-7, 2010. Crossref
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Bognet Brice, Leygue Adrien, Chinesta Francisco, On the fully 3D simulations of thermoelastic models defined in plate and shell geometries, European Journal of Computational Mechanics, 21, 1-2, 2012. 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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Prulière Etienne, Férec Julien, Chinesta Francisco, Ammar Amine, An efficient reduced simulation of residual stresses in composite forming processes, International Journal of Material Forming, 3, S2, 2010. 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, PGD-Based Computational Homogenization, in PGD-Based Modeling of Materials, Structures and Processes, 2014. Crossref
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Alberti Anthony L., Palmer Todd S., Reduced-Order Modeling of Nuclear Reactor Kinetics Using Proper Generalized Decomposition, Nuclear Science and Engineering, 194, 10, 2020. Crossref
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Oulghelou Mourad, Allery Cyrille, Mosquera Rolando, Parametric reduced order models based on a Riemannian barycentric interpolation, International Journal for Numerical Methods in Engineering, 122, 22, 2021. Crossref
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Quaranta G., Bognet B., Ibañez R., Tramecon A., Haug E., Chinesta F., A new hybrid explicit/implicit in-plane-out-of-plane separated representation for the solution of dynamic problems defined in plate-like domains, Computers & Structures, 210, 2018. Crossref
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Chipot Michel, Hackbusch Wolfgang, Sauter Stefan, Veit Alexander, Numerical Approximation of Poisson Problems in Long Domains, Vietnam Journal of Mathematics, 50, 2, 2022. Crossref
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Megdoud Abdelhak, Manser Belkacem, Belaidi Idir, Bakir Farid, Khelladi Sofiane, A reduced-order method with PGD for the analysis of dynamically loaded journal bearing, Comptes Rendus. Mécanique, 350, G2, 2022. Crossref