  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.
