Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov–Poisson equation
- 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 based on its interpretation as a tangent space projector splitting scheme. 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.
| Author: | André UschmajewGND, Andreas Zeiser |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1259250 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/125925 |
| ISSN: | 0006-3835OPAC |
| ISSN: | 1572-9125OPAC |
| Parent Title (English): | BIT Numerical Mathematics |
| Publisher: | Springer Science and Business Media LLC |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2025 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/10/21 |
| Volume: | 65 |
| Issue: | 4 |
| First Page: | 43 |
| DOI: | https://doi.org/10.1007/s10543-025-01085-6 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Mathematical Data Science | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
