Asymptotic-Preserving Numerical Schemes for the Semiconductor Boltzmann Equation Efficient in the High Field Regime

2013 ◽  
Vol 35 (3) ◽  
pp. B799-B819 ◽  
Author(s):  
Shi Jin ◽  
Li Wang
Keyword(s):  
Boltzmann Equation ◽  
High Field ◽  
Numerical Schemes ◽  
Asymptotic Preserving ◽  
Semiconductor Boltzmann Equation

THE HIGH FIELD ASYMPTOTICS FOR DEGENERATE SEMICONDUCTORS

2001 ◽  
Vol 11 (07) ◽  
pp. 1253-1272 ◽  
Author(s):  
N. BEN ABDALLAH ◽  
H. CHAKER
Keyword(s):  
Boltzmann Equation ◽  
Hyperbolic Equation ◽  
Unique Solution ◽  
High Field ◽  
Limit Problem ◽  
Nonlinear Hyperbolic Equation ◽  
Field Limit ◽  
Degenerate Semiconductors ◽  
Semiconductor Boltzmann Equation

The high field limit for the semiconductor Boltzmann equation with Pauli exclusion terms is investigated. The limit problem is shown to have a unique solution for every given density. The proof relies on a linearization procedure together with a continuation argument. The density is finally proven to converge in the high field limit towards the solution of a nonlinear hyperbolic equation.

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