Alternative computational methods for Boltzmann and Wigner models in charged transport systems

We will discuss recent development in the simulation of Boltzmann-Poisson systems and Wigner transport by deterministic numerical solvers. We have proposed to solve linear transport problems using a Discontinuous Galerkin (DG) Finite Element Method (FEM) approach that allows adaptivity and accuracy by a flexible choice of basis functions, as well as numerical efficiency by parallelization and scalability. In the case of non-linear transport, spectral methods may be competitive for the calculation of anisotropic scattering. Such numerical schemes can be competitive to DSMC methods and have the advantage of an easy and accurate implementation of boundary conditions including charge neutrality at contacts and specular and diffusive reflection at insulating and interface boundaries. These deterministic solvers are able to resolve small scales (or order 10^-7 to 10^-6) that DSMC approach may not be able to handle.