405 research outputs found
High order and energy preserving discontinuous Galerkin methods for the Vlasov-Poisson system
We present a computational study for a family of discontinuous Galerkin
methods for the one dimensional Vlasov-Poisson system that has been recently
introduced. We introduce a slight modification of the methods to allow for
feasible computations while preserving the properties of the original methods.
We study numerically the verification of the theoretical and convergence
analysis, discussing also the conservation properties of the schemes. The
methods are validated through their application to some of the benchmarks in
the simulation of plasma physics.Comment: 44 pages, 28 figure
A dynamical adaptive tensor method for the Vlasov-Poisson system
A numerical method is proposed to solve the full-Eulerian time-dependent
Vlasov-Poisson system in high dimension. The algorithm relies on the
construction of a tensor decomposition of the solution whose rank is adapted at
each time step. This decomposition is obtained through the use of an efficient
modified Progressive Generalized Decomposition (PGD) method, whose convergence
is proved. We suggest in addition a symplectic time-discretization splitting
scheme that preserves the Hamiltonian properties of the system. This scheme is
naturally obtained by considering the tensor structure of the approximation.
The efficiency of our approach is illustrated through time-dependent 2D-2D
numerical examples
A semi-Lagrangian Vlasov solver in tensor train format
In this article, we derive a semi-Lagrangian scheme for the solution of the
Vlasov equation represented as a low-parametric tensor. Grid-based methods for
the Vlasov equation have been shown to give accurate results but their use has
mostly been limited to simulations in two dimensional phase space due to
extensive memory requirements in higher dimensions. Compression of the solution
via high-order singular value decomposition can help in reducing the storage
requirements and the tensor train (TT) format provides efficient basic linear
algebra routines for low-rank representations of tensors. In this paper, we
develop interpolation formulas for a semi-Lagrangian solver in TT format. In
order to efficiently implement the method, we propose a compression of the
matrix representing the interpolation step and an efficient implementation of
the Hadamard product. We show numerical simulations for standard test cases in
two, four and six dimensional phase space. Depending on the test case, the
memory requirements reduce by a factor in four and a factor
in six dimensions compared to the full-grid method
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