TY - JOUR
T1 - Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors
AU - Giacomo Dimarco, Lorenzo Pareschi & Vittorio Rispoli
JO - Communications in Computational Physics
VL - 5
SP - 1291
EP - 1319
PY - 2014
DA - 2014/05
SN - 15
DO - http://doi.org/10.4208/cicp.090513.151113a
UR - https://global-sci.org/intro/article_detail/cicp/7138.html
KW - 
AB - <p style="text-align: justify;">In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes
for solving the multi-scale semiconductor Boltzmann equation. The relevant scale
which characterizes this kind of problems is the diffusive scaling. This means that, in
the 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 the
diffusive one. Moreover, we want to overcome the restrictive time step conditions of
standard 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 order
time and space discretization schemes which do not suffer from the usual parabolic
stiffness in the diffusive limit. We show different numerical results which permit to
appreciate the performances of the proposed schemes.</p>