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 talk, we will construct adaptive and hybrid       sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein model.  This model has applications to plasma physics and is simulated in 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.  The method utilizes a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria.  We will 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. Results of this talk are obtained using the adaptive sparse-grid discretization library Adaptive Sparse Grid Discretization.

Speaker’s Bio:  Stefan Schnake is a research scientist in the Multiscale Methods and Dynamics Group. He received his Ph.D. in 2017 from the University of Tennessee and joined Oak Ridge National Laboratory in 2020 after a postdoctoral appointment at the University of Oklahoma.  His research interests include low-rank and sparse-grid methods for compressing tensor representations of solutions to dynamical systems.