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.
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Support from the Institute of Computational Engineering and Sciences and the University of Texas Austin is gratefully acknowledged. Research supported for the first author by NSF grant DMS-1016001. Research supported for the second author by NSF grant DMS-0807712 and DMS-0757450. Research supported for the third author by PRA 2009 Unict. Research supported for the fourth author by NSF grant DMS-0809086 and DOE grant DE-FG02-08ER25863.
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Cheng, Y., Gamba, I.M., Majorana, A. et al. A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations. SeMA 54, 47–64 (2011). https://doi.org/10.1007/BF03322587
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DOI: https://doi.org/10.1007/BF03322587