On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition
Language
en
Article de revue
This item was published in
Mathematics and Computers in Simulation. 2010-12, vol. 81, n° 4, p. 791-810
Elsevier
English Abstract
This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in ...Read more >
This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in meshbased discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encountered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schr¨odinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker-Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, ... This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations.Read less <
English Keywords
Multidimensional models
Curse of dimensionality
Parametric models
Proper Generalized Decompositions
Separated representations
Origin
Hal imported