On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition

Prulière, Etienne; Chinesta, Francisco; Ammar, Amine

doi:10.1016/j.matcom.2010.07.015

Cited by 101 publications

(97 citation statements)

References 22 publications

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“…The PGD method is therefore able to obtain solutions for any value of the parameters at any point of the space, at any time instant [39,61]. So to speak, PGD provides the analyst with a sort of meta-model, but with the strong novelty of not needing any previous computer experiments.…”

Section: Proper Generalized Decomposition: a Brief Summarymentioning

confidence: 99%

Real-time simulation techniques for augmented learning in science and engineering

et al. 2015

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In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.Peer ReviewedPostprint (author's final draft

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Section: Proper Generalized Decomposition: a Brief Summarymentioning

confidence: 99%

Real-time simulation techniques for augmented learning in science and engineering

et al. 2015

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“…The foundations and some recent advances in the proper generalized decomposition based discretization strategies can be found in [1][2][3][4][5][6][7][8][9][10][11][12][19][20][21][22][23][24][25][26][27][28][29][30][31][32]35] and the references therein.…”

Section: Towards Generalized Parametric Modellingmentioning

confidence: 99%

Proper Generalized Decomposition Based Dynamic Data-Driven Control of Material Forming Processes

Ghnatios¹,

Masson²,

Leygue³

et al. 2011

AIP Conference Proceedings

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a b s t r a c tDynamic Data-Driven Application Systems-DDDAS-appear as a new paradigm in the field of applied sci-ences and engineering, and in particular in Simulation-based Engineering Sciences. By DDDAS we mean a set of techniques that allow to link simulation tools with measurement devices for real-time control of systems and processes. In this paper a novel simulation technique is developed with an eye towards its employ in the field of DDDAS. The main novelty of this technique relies in the consideration of param-eters of the model as new dimensions in the parametric space. Such models often live in highly multidi-mensional spaces suffering the so-called curse of dimensionality. To avoid this problem related to mesh-based techniques, in this work an approach based upon the Proper Generalized Decomposition-PGD-is developed, which is able to circumvent the redoubtable curse of dimensionality. The approach thus developed is composed by a marriage of DDDAS concepts and a combination of PGD ''off-line'' com-putations, linked to ''on-line'' postprocessing. In this work we explore some possibilities in the context of process control, malfunctioning identification and system reconfiguration in real time, showing the potentialities of the technique in real engineering contexts.

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“…In practice, modes are calculated successively, which is termed as the enrichment procedure. During each enrichment, simultaneously determining all vectors in the array leads to a nonlinear problem that can be effectively computed using the alternating direction method (ADM) which is sometimes named the fixed point iteration procedure [6]. Advantage of the PGD approach is twofold.…”

Section: Introductionmentioning

confidence: 99%

Application of PGD on Parametric Modeling of a Piezoelectric Energy Harvester

et al. 2016

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In this paper, a priori model reduction methods via low-rank tensor approximation are introduced for the parametric study of a piezoelectric energy harvester (EH). The EH, comprised of a cantilevered piezoelectric bimorph connected with electrical loads, is modeled using three dimensional finite elements (FEs). Solving the model for various excitation frequencies and electrical load using the conventional approach results in a large size problem that is costly in terms of CPU time. We propose an approach based on the proper generalized decomposition (PGD) that can effectively reduce the problem size with a good accuracy of the solutions. With the proposed approach, field variables of the coupled problem are decomposed into space, frequency and electrical load associated components. To introduce PGD into the FE model, a method to model the electrodes and electrical charges in the EH is presented. Appropriate choice for stopping criterions in the method, as well as accelerating the convergence through updating after each enrichment are investigated. The proposed method is validated through a representative numerical example.

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On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition

Cited by 101 publications

References 22 publications

Real-time simulation techniques for augmented learning in science and engineering

Real-time simulation techniques for augmented learning in science and engineering

Proper Generalized Decomposition Based Dynamic Data-Driven Control of Material Forming Processes

Application of PGD on Parametric Modeling of a Piezoelectric Energy Harvester

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