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Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors

Published online by Cambridge University Press:  03 June 2015

Giacomo Dimarco ,
Lorenzo Pareschi  and
Vittorio Rispoli
Giacomo Dimarco*
Affiliation:
Université de Toulouse; UPS, INSA, UT1, UTM; CNRS, UMR 5219; Institut de Mathématiques de Toulouse; F-31062 Toulouse, France
Lorenzo Pareschi*
Affiliation:
Department of Mathematics and Computer Science, University of Ferrara, via Machiavelli 35, 44121 Ferrara, Italy
Vittorio Rispoli*
Affiliation:
Department of Mathematics and Computer Science, University of Ferrara, via Machiavelli 35, 44121 Ferrara, Italy
*
Email:giacomo.dimarco@math.univ-toulouse.fr
Email:lorenzo.pareschi@unife.it
Corresponding author.Email:vittorio.rispoli@unife.it
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Abstract

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.

Keywords

35B2565M0676R5082C70IMEX-RK methodsasymptotic preserving methodssemiconductor Boltzmann equationdrift-diffusion limit
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1291 - 1319
Copyright
Copyright © Global Science Press Limited 2014

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