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A dynamic Low-rank approximation for the Vlasov equation Einkemmer, Lukas Dec 6, 2018
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Title | A dynamic Low-rank approximation for the Vlasov equation |
Creator |
Einkemmer, Lukas |
Publisher | Banff International Research Station for Mathematical Innovation and Discovery |
Date Issued | 2018-12-06T13:31 |
Description | Many problems encountered in plasma physics require a kinetic description. The associated partial differential equations are posed in an up to six-dimensional phase space. A direct discretization of this phase space, often called the Eulerian approach, has many advantages but is extremely expensive from a computational point of view. In this talk we propose a dynamical low-rank approximation to the Vlasov equation. This approximation is derived by constraining the dynamics to a manifold of low-rank functions via a tangent space projection. Then the projection is split into the sub-projections from which it is built. This reduces a time step for the six- (or four-) dimensional Vlasov--Poisson equation to solving two systems of three- (or two-) dimensional advection equations. This projector-splitting approach also enables us to dynamically adjust the rank during the simulation. |
Extent | 34.0 |
Subject |
Mathematics Numerical analysis Partial differential equations Scientific computing |
Geographic Location | Banff (Alta.) |
Type |
Moving Image |
FileFormat | video/mp4 |
Language | eng |
Notes | Author affiliation: University of Innsbruck |
Series | BIRS Workshop Lecture Videos (Banff, Alta) |
Date Available | 2019-06-05 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0379284 |
URI | http://hdl.handle.net/2429/70507 |
Affiliation |
Non UBC |
Peer Review Status | Unreviewed |
Scholarly Level | Researcher |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
AggregatedSourceRepository | DSpace |
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https://iiif.library.ubc.ca/presentation/dsp.48630.1-0379284/manifest