Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov-Poisson equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912536711921664 |
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| author | Uschmajew, André Zeiser, Andreas |
| author_facet | Uschmajew, André Zeiser, Andreas |
| contents | A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov-Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs' systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed which facilitates a projector splitting integrator. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov-Poisson equation Uschmajew, André Zeiser, Andreas Numerical Analysis 15A69, 65M60, 82D10 A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov-Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs' systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed which facilitates a projector splitting integrator. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity. |
| title | Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov-Poisson equation |
| topic | Numerical Analysis 15A69, 65M60, 82D10 |
| url | https://arxiv.org/abs/2503.10562 |