An error estimator for separated representations of highly multidimensional models

Author (s): Ammar A; Chinesta F; Díez, P and Huerta, A
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 199, Issues 25-28
Pages: 1872 – 1880
Date: 2010

Abstract:
Fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics. Most of these models consists of a partial differential equation defined in a highly multidimensional domain (e.g. Schrodinger equation, Fokker-Planck equations among many others). The main challenge related to these models is their associated curse of dimensionality. We proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations (also known as finite sums decomposition). This technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates. The issue related to error estimation has never been addressed. This paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques.

Journal paper (from the publisher)  
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Bibtex:

@article{PC-ACDH:10,
  Author   = {Ammar, A. and Chinesta, F. and Diez, P. and Huerta, A.},
  Title    = {An error estimator for separated representations of highly multidimensional models},
  Fjournal = {Computer Methods in Applied Mechanics and Engineering},
  Journal  = {Comput. Methods Appl. Mech. Eng.},
  Volume   = {199},
  Number   = {25-28},
  Pages    = {1872--1880},
  Year     = {2010},
  Doi      = {10.1016/j.cma.2010.02.012},
  Url      = {http://dx.doi.org/10.1016/j.cma.2010.02.012}}