An overview of the proper generalized decomposition with applications in computational rheology
Article dans une revue avec comité de lecture
We review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al.  and , the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates.
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Article dans une revue avec comité de lectureSCHEUER, Adrien; AMMAR, Amine; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elías; CHINESTA, Francisco; KEUNINGS, Roland; ADVANI, Suresh G. (Tech Science Press, 2018)Describing the orientation state of the particles is often critical in fibre suspension applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred ...
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Article dans une revue avec comité de lectureAMMAR, Amine; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco; KEUNINGS, Roland (Springer Verlag, 2016)Permeability is the fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium. Composite processing models require the permeability as input data to predict flow ...
Article dans une revue avec comité de lectureREILLE, Agathe; HASCOËT, Nicolas; GHNATIOS, Chady; AMMAR, Amine; CUETO, Elías G.; DUVAL, Jean Louis; CHINESTA, Francisco; KEUNINGS, Roland (Elsevier Masson, 2019)The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then ...