Space-time discretization of series expansion methods for the Boltzmann transport equation

SIAM Journal on Numerical Analysis

Volumn 38, Issue 2, 2001, Pages 442-465

  Ringhofer, Christian ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Boltzmann equation; Finite differences; Galerkin methods

Indexed keywords

EID: 0034449740     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142998339921     Document Type: Article

References (16)

1. A. ARNOLD AND C. RINGHOFER, Operator splitting methods applied to spectral discretizations of quantum transport equations, SIAM J. Numer. Anal., 32 (1995), pp. 1876-1894.
2. A. ARNOLD AND C. RINGHOFER, An operator splitting method for the Wigner-Poisson problem, SIAM J. Numer. Anal., 33 (1996), pp. 1622-1643.
3. N. ASHCROFT AND M. MERMIN, Solid State Physics, Holt-Saunders, New York, 1976.
4. N. GOLDSMAN, L. HENRICKSON, AND J. FREY, A physics based analytical-numerical solution to the Boltzmann equation for use in semiconductor device simulation, Solid State Electr., 34 (1991), p. 389.
5. A. KLAR, A numerical method for kinetic semiconductor equations in the drift diffusion limit, SIAM J. Sci. Comput., 20 (1999), pp. 1696-1712.
6. A. KLAR, An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit, SIAM J. Numer. Anal., 35 (1998), pp. 1073-1094.
7. A. KLAR, Asymptotic-induced domain decomposition methods for kinetic and drift diffusion semiconductor equations, SIAM J. Sci. Comput., 19 (1998), pp. 2032-2050.
8. D. LEVERMORE, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), pp. 1021-1065.
9. C. D. LEVERMORE AND W. J. MOROKOFF, The Gaussian moment closure for gas dynamics, SIAM J. Appl. Math., 59 (1998), pp. 72-96.
10. P. MARKOWICH, C. RINGHOFER, AND C. SCHMEISER, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
11. F. POUPAUD, Diffusion approximation of the linear Boltzmann equation: Analysis of boundary layers, Asymptotic Anal., 4 (1991), pp. 293-317.
12. C. SCHMEISER AND A. ZWIRCHMAYR, Galerkin methods for the semiconductor Boltzmann equation, in Proceedings of the International Congress of Industrial and Applied Mathematics 95, Hamburg, 1995.
13. C. SCHMEISER AND A. ZWIRCHMAYR, Convergence of moment methods for the semiconductor Boltzmann equation, SIAM J. Numer. Anal., to appear.
14. S. SELBERHERR, Analysis of Semiconductor Devices, 2nd ed., Wiley, New York, 1981.
15. D. VENTURA, A. GNUDI, AND G. BACCARANI, One dimensional simulation of a bipolar transistor by means of spherical harmonics expansions of the Boltzmann equation, in Proceedings SISDEP 91 Conference Zurich, W. Fichtner, ed., 1991, pp. 203-205.
16. D. VENTURA, A. GNUDI, G. BACCARANI, AND F. ODEH, Multidimensional spherical harmonics expansions for the Boltzmann equation for transport in semiconductors, Appl. Math. Lett., 5 (1992), pp. 85-90.