SUPG-based stabilization of Proper Generalized Decompositions for the high-dimensional Advection-Diffusion Equations

Author (s): Gonzalez, D.; Cueto, E.; Chinesta, F; Díez, P.; and Huerta, A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 94, Issue: 13
Pages: 1216 – 1232
Date: 2013

This work is a first attempt to address efficient stabilizations of high dimensional advection–diffusion models encountered in computational physics. When addressing multidimensional models, the use of mesh-based discretization fails because the exponential increase of the number of degrees of freedom related to a multidimensional mesh or grid, and alternative discretization strategies are needed. Separated representations involved in the so-called proper generalized decomposition method are an efficient alternative as proven in our former works; however, the issue related to efficient stabilizations of multidimensional advection–diffusion equations has never been addressed to our knowledge. Thus, this work is aimed at extending some well-experienced stabilization strategies widely used in the solution of 1D, 2D, or 3D advection–diffusion models to models defined in high-dimensional spaces, sometimes involving tens of coordinates.



@article {NME:NME4493,
Author = {David Gonz{\'a}lez and El{\'\i}as Cueto and Francisco Chinesta and Pedro D{\'\i}ez and Antonio Huerta},
title = {Streamline upwind/Petrov–Galerkin-based stabilization of proper generalized decompositions for high-dimensional advection–diffusion equations},
journal = {International Journal for Numerical Methods in Engineering},
volume = {94},
number = {13},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.4493},
doi = {10.1002/nme.4493},
pages = {1216--1232},
year = {2013},