Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929307781169152 |
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| author | Uschmajew, André Zeiser, Andreas |
| author_facet | Uschmajew, André Zeiser, Andreas |
| contents | We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov--Poisson equations based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. We propose a variational formulation of the projector splitting which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01856 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary Uschmajew, André Zeiser, Andreas Numerical Analysis 15A69, 65M60, 82D10 We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov--Poisson equations based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. We propose a variational formulation of the projector splitting which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach. |
| title | Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary |
| topic | Numerical Analysis 15A69, 65M60, 82D10 |
| url | https://arxiv.org/abs/2303.01856 |