Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model
Abstract
Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov-Poisson-Lenard-Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.
Cite
@article{arxiv.2402.06493,
title = {Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model},
author = {Stefan Schnake and Coleman Kendrick and Eirik Endeve and Miroslav Stoyanov and Steven Hahn and Cory D Hauck and David L Green and Phil Snyder and John Canik},
journal= {arXiv preprint arXiv:2402.06493},
year = {2024}
}