On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition
TypeArticles dans des revues avec comité de lecture
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 mesh-based 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 encoun- tered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schrödinger 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, etc. 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.
Files in this item
Showing items related by title, author, creator and subject.
Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers PRULIERE, Etienne; AMMAR, Amine; EL KISSI, Nadia; CHINESTA, Francisco (Springer Link, 2009)Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked ...
PRULIERE, Etienne; AMMAR, Amine; CHINESTA, Francisco (Lavoisier, 2007)This work focuses on the resolution of the Fokker-Planck equation that governs the evolution of the fibers orientation distribution. To reduce the computing time, that equation is solved along some flow trajectories in ...
PRULIERE, Etienne; CHINESTA, Francisco; AMMAR, Amine; LEYGUE, Adrien; POITOU, Arnaud (ELSEVIER, 2013)This papers addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, ... The first issue ...
PRULIERE, Etienne; CHINESTA, Francisco; AMMAR, Amine; LEYGUE, Adrien; POITOU, Arnaud (ELSEVIER, 2012)This paper addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, / The first issue ...
METOUI, Sondes; PRULIERE, Etienne; AMMAR, Amine; DAU, Frédéric; IORDANOFF, Ivan (Wiley, 2014)The use of cohesive zone models is an efficient way to treat the damage, especially when the crack path is known a priori. This is the case in the modeling of delamination in composite laminates. However, the simulations ...