Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model
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arXiv
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| Hauptverfasser: | , , , , , , , , |
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| Format: | Preprint |
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2024
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| author | Schnake, Stefan Kendrick, Coleman Endeve, Eirik Stoyanov, Miroslav Hahn, Steven Hauck, Cory D Green, David L Snyder, Phil Canik, John |
| author_facet | Schnake, Stefan Kendrick, Coleman Endeve, Eirik Stoyanov, Miroslav Hahn, Steven Hauck, Cory D Green, David L Snyder, Phil Canik, John |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model Schnake, Stefan Kendrick, Coleman Endeve, Eirik Stoyanov, Miroslav Hahn, Steven Hauck, Cory D Green, David L Snyder, Phil Canik, John Numerical Analysis 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. |
| title | Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.06493 |