Moment methods for the semiconductor Boltzmann equation on bounded position domains

Christian Ringhofer, C. Schmeiser, A. Zwirchmayer

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

Galerkin methods for the semiconductor Boltzmann equation based on moment expansions for a discretization in the velocity direction are studied. For the moment equations, boundary conditions are proposed, which are analogues to inflow and, respectively, reflecting boundary conditions for the Boltzmann equation. Stability and an error estimate are proved for an expansion in terms of Hermite polynomials. Finally, an adaptive numerical implementation is introduced and results of numerical experiments are presented.

Original languageEnglish (US)
Pages (from-to)1078-1095
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume39
Issue number3
DOIs
StatePublished - 2002

Fingerprint

Moment Method
Boltzmann equation
Method of moments
Boltzmann Equation
Semiconductors
Boundary conditions
Semiconductor materials
Moment Equations
Hermite Polynomials
Galerkin methods
Galerkin Method
Error Estimates
Discretization
Numerical Experiment
Polynomials
Moment
Analogue
Experiments

Keywords

  • Boltzmann equation
  • Moment expansion
  • Semiconductors

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Moment methods for the semiconductor Boltzmann equation on bounded position domains. / Ringhofer, Christian; Schmeiser, C.; Zwirchmayer, A.

In: SIAM Journal on Numerical Analysis, Vol. 39, No. 3, 2002, p. 1078-1095.

Research output: Contribution to journalArticle

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