Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices

Yunxian Liu Shandong University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25019

Science China Mathematics, 59, 115-140, 2016
In this paper we consider the drift-diffusion (DD) model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Poisson potential equation. Optimal error estimates are obtained for both the semi-discrete and fully discrete local discontinuous Galerkin (LDG) schemes with smooth solutions. In the fully discrete scheme, we couple the implicit-explicit (IMEX) time discretization with the LDG spatial discretization, in order to allow larger time steps and to save computational cost. The main technical difficulty in the analysis is to treat the inter-element jump terms which arise from the discontinuous nature of the numerical method and the nonlinearity and coupling of the models. A simulation is also performed to validate the analysis.
Local discontinuous Galerkin method, Semi-discrete, Implicit-explicit scheme, Error estimate, Semiconductor
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@inproceedings{yunxian2016analysis,
  title={Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices},
  author={Yunxian Liu, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011111156930875133},
  booktitle={Science China Mathematics},
  volume={59},
  pages={115-140},
  year={2016},
}
Yunxian Liu, and Chi-Wang Shu. Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices. 2016. Vol. 59. In Science China Mathematics. pp.115-140. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011111156930875133.
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