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Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary
André Uschmajew, Andreas Zeiser
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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.
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