Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 281, Issue -, Pages 806-824Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.10.050
Keywords
Semiconductor Boltzmann equation; Energy-transport system; Asymptotic-preserving scheme; Fast spectral method
Funding
- CSCAMM, University of Maryland
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1107291] Funding Source: National Science Foundation
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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. (C) 2014 Elsevier Inc. All rights reserved.
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