Volume 15, Issue 5
Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors

Giacomo Dimarco, Lorenzo Pareschi & Vittorio Rispoli

Commun. Comput. Phys., 15 (2014), pp. 1291-1319.

Published online: 2014-05

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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.

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@Article{CiCP-15-1291, author = {}, title = {Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1291--1319}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.090513.151113a}, url = {http://global-sci.org/intro/article_detail/cicp/7138.html} }
TY - JOUR T1 - Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors 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 -

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.

Giacomo Dimarco, Lorenzo Pareschi & Vittorio Rispoli. (2020). Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors. Communications in Computational Physics. 15 (5). 1291-1319. doi:10.4208/cicp.090513.151113a
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