A wavelet method to solve high-dimensional transport equations in semiconductor devices

The Multi-Wavelet (MW) Discontinuous Galerkin method (DG) (MWDG) for high polynomial orders (POs) is proposed for the solution of 6-dimensional transport equations for the first time. In contrast to the popular Spherical Harmonics expansion method (SHE), the DG formulation is stable under the application of high order piecewise polynomials (pp) in energy and real space dimensions which turn out to clearly outperform piecewise constants (pc). MWs build a hierarchical basis for all piecewise polynomials (pps) so that the MWDG and the usual nodal DG (NDG) can be equivalent. However, in the MWDG it is possible to reduce the problem to small adaptively compressed sub spaces which strongly reduces the computational costs at only a small expense of accuracy. The increasing TCAD challenges for the simulation of new 3-dimensional nano-devices could be approached by efficient MWDG Boltzmann and Wigner solvers.