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

Abstract

his 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.