  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.
