Abstract Details
Abstracts
Author: David L Green
Requested Type: Poster
Submitted: 2019-02-22 16:42:05
Co-authors: L. Mu, E.F. D'Azevedo, M.G. Lopez, W. Elwasif, B.T. McDaniel, T.R. Younkin, A. Haidar, D. del-Castillo-Negrete
Contact Info:
Oak Ridge National Laboratory
1 Bethel Valley Road
Oak Ridge, TN 37831
USA
Abstract Text:
Magnetic confinement fusion admits many high dimensional PDEs whose numerical solution becomes challenging due to the so-called curse of dimensionality where the scaling of the degrees of freedom goes as O(N^d). Here we present an arbitrarily high-order discontinuous-Galerkin finite-element solver built atop an adaptive sparse-grid discretization whose degrees of freedom scale as O(N|log2N|d-1). We will demonstrate the application of this method, and its subsequent reduction in the required resources, to several PDEs including time-domain Maxwell's equations (3D), the Vlasov equation (in up to 6D) and a Fokker-Planck-like problem. The computational performance of both explicit and implicit time advance algorithms will be discussed with particular emphasis on GPU efficiency.
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