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A dynamic Low-rank approximation for the Vlasov equation

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Numerical analysis; Partial differential equations; Scientific computing

video/mp4

Author affiliation: University of Innsbruck

2019-06-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70507

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/