Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors (Communications in Computational Physics, 2014)
In this paper we develop a class of Implicit-Explicit Runge-Kutta schemesfor solving the multi-scale semiconductor Boltzmann equation. The relevant scalewhich characterizes this kind of problems is the diffusive scaling. This means that, inthe limit of zero mean free path, the system is governed by a drift-diffusion equation.Our aim is to develop a method which accurately works for the different regimes encountered in general semiconductor simulations: the kinetic, the intermediate and thediffusive one. Moreover, we want to overcome the restrictive time step conditions ofstandard time integration techniques when applied to the solution of this kind of phenomena without any deterioration in the accuracy. As a result, we obtain high ordertime and space discretization schemes which do not suffer from the usual parabolicstiffness in the diffusive limit. We show different numerical results which permit toappreciate the performances of the proposed schemes.