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SeMA Journal

, Volume 54, Issue 1, pp 47–64 | Cite as

A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations

  • Yingda Cheng
  • Irene M. Gamba
  • Armando Majorana
  • Chi-Wang Shu
Article

Abstract

We are interested in the deterministic computation of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The main difficulty of such computation arises from the very high dimensions of the model, making it necessary to use relatively coarse meshes and hence requiring the numerical solver to be stable and to have good resolution under coarse meshes. In this paper we give a brief survey of the discontinuous Galerkin (DG) method, which is a finite element method using discontinuous piecewise polynomials as basis functions and numerical fluxes based on upwinding for stability, for solving the Boltzmann-Poisson system. In many situations, the deterministic DG solver can produce accurate solutions with equal or less CPU time than the traditional DSMC (Direct Simulation Monte Carlo) solvers. In order to make the presentation more concise and to highlight the main ideas of the algorithm, we use a simplified model to describe the details of the DG method. Sample simulation results on the full Boltzmann-Poisson system are also given.

Keywords

Coarse Mesh Discontinuous Galerkin Discontinuous Galerkin Method Direct Simulation Monte Carlo Boltzmann Transport Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Sociedad Española de Matemática Aplicada 2011

Authors and Affiliations

  • Yingda Cheng
    • 1
  • Irene M. Gamba
    • 1
  • Armando Majorana
    • 2
  • Chi-Wang Shu
    • 3
  1. 1.Department of Mathematics and ICESUniversity of Texas at AustinUSA
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CataniaItaly
  3. 3.Division of Applied MathematicsBrown UniversityUSA

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