Streamline upwind/Petrov-Galerkin-Based Stabilization of Proper Generalized Decompositions for High-Dimensional Advection-Diffusion Equations
Résumé
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.
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