An overview of the proper generalized decomposition with applications in computational rheology

被引:192
作者
Chinesta, F. [1 ]
Ammar, A. [2 ]
Leygue, A. [1 ]
Keunings, R. [3 ]
机构
[1] UMR CNRS Cent Nantes, EADS Corp Fdn Int Chair, GEM, F-44321 Nantes 3, France
[2] Arts & Metiers ParisTech, F-49035 Angers 01, France
[3] Catholic Univ Louvain, ICTEAM, B-1348 Louvain, Belgium
关键词
Complex fluids; Numerical modeling; Model reduction; Proper orthogonal decomposition; Proper generalized decomposition; Kinetic theory; Parametric models; Optimization; Inverse identification; PRIORI MODEL-REDUCTION; KINETIC-THEORY MODELS; COMPLEX FLUIDS; SIMULATION; SOLVERS; FAMILY;
D O I
10.1016/j.jnnfm.2010.12.012
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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. [3,4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrodinger 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. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:578 / 592
页数:15
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