Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model
<|reference_start|>Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model: 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.<|reference_end|>
@article{schnake2024sparse-grid,
    title={Sparse-grid Discontinuous Galerkin Methods for the
  Vlasov-Poisson-Lenard-Bernstein Model},
    author={Stefan Schnake, Coleman Kendrick, Eirik Endeve, Miroslav Stoyanov,
  Steven Hahn, Cory D Hauck, David L Green, Phil Snyder, John Canik},
    journal={arXiv preprint arXiv:2402.06493},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06493},
    primaryClass={math.NA cs.NA}
}