Semi-Lagrangian schemes for the two-dimensional Vlasov-Poisson system on unstructured meshes

In this article, we present new high-order, semi-Lagrangian schemes for solving the Vlasov-Poisson system on an unstructured four-dimensional phase-space mesh. The method is based on the propagation of the distribution function and its jacobian by following the characteristic curves backward. Then the distribution function is reconstructed using high-order and few diffusive interpolation operators coming from the finite element and the computer aided geometric design (CAGD) literature. Numerical tests in plasma physics and charged-particle beam transport are investigated.