Abstract
Recently the authors have developed and successfully applied a continuation technique for the numerical solution of parameter-dependent nonlinear elliptic boundary value problems. The method was integrated into an existing multi-grid package based on an adaptive finite element discretization. An extension to nonlinear systems of differential equations is considered. Since one important field of application is the VLSI device simulation we discuss this problem and present preliminary numerical results for a MOSFET device.
Keywords
- Continuation Method
- Device Simulation
- Single Precision
- Nonlinear Elliptic System
- Continuation Technique
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The work of the first author was supported by the Office of Naval Research under Grant N00014-82-K-0197. The second author was supported by the Air Force Office of Scientific Research under Grant AFOSR-84-0315.
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References
R.E. Bank, PLTIMG User's Guide, Edition 4.0, Tech. Report, Dept. Math., University of California, San Diego (1985).
R.E. Bank, D.J. Rose and W. Fichtner, Numerical Methods for Semiconductor Device Simulation, SIAM J. Sci. Stat. Comp. 4, 416–435 (1983) and IEEE Trans. Electron Devices, Vol. ED-30, 1031–1041 (1983).
R.E. Bank, W.M. Coughran, Jr., W. Fichtner, D.J. Rose and R.K. Smith, Computational Aspects of Semiconductor Device Simulation, Numerical Analysis Manuscript 85-3, AT&T Bell Laboratories, Murray Hill, NJ 07974.
R.E. Bank, W.M. Coughran, Jr., W. Fichter, E.H. Grosse, D.J. Rose and R.K. Smith, Transient Simulation of Silicon Devices and Circuits, Numerical Analysis Manuscript 85-8, AT&T Bell Laboratories, Murray Hill, NJ 07974.
R.E. Bank and T.F. Chan, PLTMGC: A Multi-grid Continuation Program for Parametrized Nonlinear Elliptic Systems, SIAM J. Sci. Stat. Comp. 3, 173–194 (1982).
W. Fichtner, D.J. Rose and R.E. Bank, Semiconductor Device Simulation, SIAM J. Sci. Stat. Comp. 4, 391–415 (1983) and IEEE Trans. Electron Devices, Vol. ED-30, 1018–1030 (1983).
W. Hackbusch, Multi-grid Solution of Continuation Problems, in "Iterative Solution of Non-linear Systems (R. Ansorge, T. Meis, W. Törnig, eds.), Lecture Notes in Mathematics 953, Springer-Verlag, Berlin (1982).
P.A. Markowich, C.A. Ringhofer and A. Steindl, Computation of Current-Voltage Characteristics using Arclength Continuation, IMA J. Appl. Math. 33, 175–187 (1984).
H.D. Mittelmann, Multi-grid methods for simple Bifurcation Problems, in "Multi-grid Methods (W. Hackbusch, U. Trottenberg, eds.), Lecture Notes in Mathematics 960, Springer-Verlag, Berlin (1982).
H.D. Mittelmann, Multi-level Continuation Techniques for Nonlinear Boundary Value Problems with Parameter Dependence, Tech. Report No. 85, Dept. Math., Arizona State University, Tempe, AZ 85287 (1985) (to appear in Appl. Math. Comp.).
H.D. Mittelmann, A Pseudo-Arclength Continuation Method for Nonlinear Eigenvalue Problems (submitted to SIAM J. Numer. Anal.) (1985).
H.D. Mittelmann, Continuation near Symmetry-Breaking Bifurcation Points, in "Numerical Methods for Bifurcation Problems" (T. Küpper, H.D. Mittelmann, H. Weber, eds.), ISNM 70, Birkhäuser-Verlag, Basel (1984).
W.C. Rheinboldt and J.V. Burkhardt, A locally parametrized Continuation Process, ACM Trans. Math. Software 9, 215–235 (1983).
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© 1986 Springer-Verlag
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Bank, R.E., Mittelmann, H.D. (1986). Continuation and multi-grid for nonlinear elliptic systems. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods II. Lecture Notes in Mathematics, vol 1228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072639
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DOI: https://doi.org/10.1007/BFb0072639
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