An efficient ‘a priori’ model reduction for boundary element models

Ryckelynck, David; Hermanns, Ludger M.; Chinesta, Francisco; Alarcón, Enrique

doi:10.1016/j.enganabound.2005.04.003

Cited by 42 publications

(36 citation statements)

References 8 publications

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“…The interested readers can reefer to [2, 5, 15, 20, 36, 58, 60-63, 67, 74] and the numerous references therein. The extraction of the reduced basis is the tricky point when using POD-based model order reduction, as well its adaptivity when addressing scenarios far from the ones considered when constructing the reduced basis [72,73]. Another issue lies in the error control, and its connection with verification and validation.…”

Section: Fast Calculations From a Historical Perspectivementioning

confidence: 99%

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

Chinesta

Leygue²,

Bordeu³

et al. 2013

Arch Computat Methods Eng

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291

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to highdimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with highdimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

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Section: Fast Calculations From a Historical Perspectivementioning

confidence: 99%

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

Chinesta

Leygue²,

Bordeu³

et al. 2013

Arch Computat Methods Eng

Self Cite

280

291

View full text Add to dashboard Cite

show abstract

“…These modes could be now used to solve other "similar" problems, that is, models involving slight changes in the boundary conditions, model parameters, ... [18] [14] [21]. Other possibility is computing the reduced basis from the standard transient solution within a short time interval (with respect to the whole time interval in which the model is defined) and then solve the remaining part of the time interval by employing the reduced basis.…”

Section: Motivating the Use Of Separated Space-time Representationsmentioning

confidence: 99%

Proper generalized decomposition of multiscale models

Chinesta

Ammar

Cueto

2010

Numerical Meth Engineering

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In this paper the coupling of a parabolic model with a system of local kinetic equations is analyzed. A space–time separated representation is proposed for the global model (this is simply the radial approximation proposed by Pierre Ladeveze in the LATIN framework (Non‐linear Computational Structural Mechanics. Springer: New York, 1999)). The originality of the present work concerns the treatment of the local problem, that is first globalized (in space and time) and then fully globalized by introducing a new coordinate related to the different species involved in the kinetic model. Thanks to the non‐incremental nature of both discrete descriptions (the local and the global one) the coupling is quite simple and no special difficulties are encountered by using heterogeneous time integrations. Copyright © 2009 John Wiley & Sons, Ltd.

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“…The other approach consists in solving the non-reduced model in the whole time interval, whose solution allows defining the reduced approximation basis that then could be used for solving "similar" models, as the ones that involve for example slight variations in some material parameters or in the boundary conditions. Some recent advances in such approaches can be found in [36], [31], [39], [40], [41] [9], [13], [25] and the references therein.…”

Section: The Proper Orthogonal Decomposition Revisitedmentioning

confidence: 99%

Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

Prulière

Ammar

Kissi

et al. 2008

Arch Computat Methods Eng

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. SummaryNumerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic advection equations. In non-recirculating flows, Eulerian discretizations can give a convergent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In this paper we compares different advanced strategies (some of them recently proposed and extended here for addressing complex flows) when they are applied to the solution of the kinetic theory description of a short fiber suspension fluid flows.

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An efficient ‘a priori’ model reduction for boundary element models

Cited by 42 publications

References 8 publications

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

Proper generalized decomposition of multiscale models

Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

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