Abstract
For the type of boundary value problems which figure in the drift-diffusion semiconductor model, the perpendicular-bisecting box-method discretization yields M-matrices and maximum stability on Delaunay triangulations, whereas the piecewise linear finite element discretization need not. In two dimensions this discrepancy is due to variability of coefficients in the drift-diffusion equations. In three dimensions the difference is, furthermore, of geometric origin. Some results for both dimensionalities are presented and discussed.
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References
I. Babuška and A.K. Aziz. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differentiqal Equations. Academic Press, New York, San Fransisco, London, 1972.
Randolph E. Bank and Donald J. Rose. Some Error Estimates for the Box Method. SIAM J. on Numer. Anal., 24:777–787, 1987.
Randolph E. Bank, Donald J. Rose, and Wolfgang Fichtner. Numerical Methods for Semiconductor Device Simulation. SIAM J. on Scient. and Statist. Comp., 4(3):416–435, September 1983.
Philippe G. Ciarlet. The Finite Element Method for Elliptic Problems. North Holland, Amsterdam, New York, Oxford, 1978.
B. Delaunay. Sur La Sphere Vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk, 7(6):792–800, 1932.
Herbert Edelsbrunner. Spatial Triangulations with Dihedral Angle Conditions. In Proc. Int. Workshop on Discrete Algorithms and Complexity pages 83–89, 1989.
Jörg Machel and Siegfried Selberherr. A Novel Finite Element Approach to device Modeling. IEEE TRans on Electr. Dev., ED-30(9):1083–1092, 1983.
Thomas Kerkhoven. Petrov-Galerkin Finite Element Approximation And The Box-Method. Technical report, University of Illinois, in preparation.
Thomas Kerkhoven and Joseph W. Jerome L ∞ Stability of Finite Element Approximations to Elliptic Gradient Equations. Numerische Mathematik, 57:561–575, 1990.
D. Scharfetter and H.K. Gummel. Large signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Devices, ED-20:64–77, 1969.
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© 1994 Springer Basel AG
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Kerkhoven, T. (1994). A Piecewise Linear Petrov-Galerkin Analysis of the Box-Method. In: Bank, R.E., Gajewski, H., Bulirsch, R., Merten, K. (eds) Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices. ISNM International Series of Numerical Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8528-7_17
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DOI: https://doi.org/10.1007/978-3-0348-8528-7_17
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