Asymptotic-induced domain decomposition methods for kinetic and drift diffusion semiconductor equations

SIAM Journal on Scientific Computing

Volumn 19, Issue 6, 1998, Pages 2032-2050

  Klar, Axel ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Asymptotic analysis; Domain decomposition methods; Drift diffusion equation; Kinetic semiconductor equations

Indexed keywords

DOMAIN DECOMPOSITION METHODS; DRIFT DIFFUSION EQUATION; KINETIC SEMICONDUCTOR EQUATIONS;

HYDRODYNAMICS; KINETIC THEORY; MATHEMATICAL MODELS; PROBLEM SOLVING;

ASYMPTOTIC STABILITY;

EID: 0032205976     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595286177     Document Type: Article

References (21)

1. C. BARDOS, R. SANTOS, AND R. SENTIS, Diffusion approximation and computation of the critical size, Trans. Amer. Math. Soc., 284 (1984), p. 617-649.
2. A. BENSOUSSAN, J. LIONS, AND G. PAPANICOLAOU, Boundary layers and homogenization of transport processes, Publ. Res. Inst. Math. Sci., 15 (1979), p. 52-157.
3. J. BOURGAT, P. LE TALLEC, D. TIDRIRI, AND Y. QIU, Numerical coupling of nonconservative or kinetic models with the conservative compressible Navier-Stokes equations, in Fifth International Symposium on Domain Decomposition Methods for PDEs, SIAM, Philadelphia, 1991.
4. C. CERCIGNANI, The Boltzmann Equation and Its Applications, Springer Verlag, New York 1988.
5. F. GOLSE, Applications of the Boltzmann equation within the context of upper atmosphere vehicle aerodynamics, Comput. Methods Appl. Mech. Engrg., 75 (1989), p. 299-314.
6. F. GOLSE AND A. KLAR, A numerical method for computing asymptotic states and outgoing distributions for kinetic linear half space problems, J. Statist. Phys., 80 (1995), p. 1033-1061.
7. F. GOLSE AND F. POUPAUD, Limite fluide des equations de Boltzmann des semi-conducteurs pour une statistique Fermi-Dirac, J. Asymptotic Anal., 6 (1992), p. 135-.
8. W. GREENBERG, C. VAN DER MEE, AND V. PROTOPOPESCU, Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser, Basel, 1987.
9. R. ILLNER AND H. NEUNZERT, Domain decomposition: Linking kinetic and aerodynamic descriptions, AGTM preprint, Univ. of Kaiserslautern, Germany, 1993.
10. A. KLAR, Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations, Math. Methods Appl. Sci., 18 (1995), p. 649-670.
11. A. KLAR, Domain decomposition for kinetic problems with nonequilibrium states, European J. Mech. B Fluids, 15 (1996), p. 203-216.
12. H. KOSINA, Simulation des Ladungstransportes in elektronischen Bauelementen mit Hilfe der Monte Carlo Methode, Ph.D. Thesis, TU Wien, Austria, 1992.
13. E. LARSEN, G. POMRANING, AND V. BADHAM, Asymptotic analysis of radiative transfer problems, J. Quant. Spectr. Radiative Transfer, 29 (1983), p. 285-310.
14. S. LOYALKA, Approximate method in the kinetic theory, Phys. Fluids, 14 (1971), p. 2291-2294.
15. A. LUKSCHIN, H. NEUNZERT, AND J. STRUCKMEIER, Coupling of Boltzmann and Navier Stokes Equations, Interim Report for the Hermes Project, Tech. Report DPH6174/91, ESA Project, Kaiserslautern, Germany, 1992.
16. P. MARKOWICH, C. RINGHOFER, AND C. SCHMEISER, Semiconductor equations, Springer-Verlag, Wien, Austria, 1990.
17. F. POUPAUD, Diffusion approximation of the linear semiconductor equation, J. Asymptotic Anal., 4 (1991), p. 293-317.
18. C. SCHMEISER AND A. ZWIRCHMAYR, Convergence of Moment Methods for the Semiconductor Boltzmann Equation, preprint, TU Wien, Austria, 1996.
19. S. SELBERHERR, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Wien, Austria, 1984.
20. Y. SONE, Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers, in Advances in Kinetic Theory and Continuum Mechanics, Proceedings of a Symposium Held in Honour of Henri Cabannes, R. Gatignol and Soubbaramayer, eds., Springer-Verlag, Berlin, 1990, pp. 19-31.
21. A. YAMNAHAKKI, Second order boundary conditions of drift diffusion equations of semiconductors, Math. Methods Appl. Sci., 5 (1995), p. 429-455.