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Title: An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.
Authors:
 [1] ;  [2]
  1. The Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712 (United States)
  2. Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095 (United States)
Publication Date:
OSTI Identifier:
22382170
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; BERNSTEIN MODE; BOLTZMANN EQUATION; DIFFUSION; ELECTRON COLLISIONS; MATHEMATICAL OPERATORS; MEAN FREE PATH; PLASMA WAVES; POWER TRANSMISSION; SEMICONDUCTOR MATERIALS