Moment methods for the semiconductor Boltzmann equation on bounded position domains

Christian Ringhofer, C. Schmeiser, A. Zwirchmayer

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

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

Keywords

  • Boltzmann equation
  • Moment expansion
  • Semiconductors

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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