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Continuation and multi-grid for nonlinear elliptic systems

  • R. E. Bank
  • H. D. Mittelmann
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1228)

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.

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References

  1. [1]
    R.E. Bank, PLTIMG User's Guide, Edition 4.0, Tech. Report, Dept. Math., University of California, San Diego (1985).Google Scholar
  2. [2]
    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).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    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).CrossRefGoogle Scholar
  6. [6]
    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).MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    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).Google Scholar
  8. [8]
    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).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    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).Google Scholar
  10. [10]
    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.).Google Scholar
  11. [11]
    H.D. Mittelmann, A Pseudo-Arclength Continuation Method for Nonlinear Eigenvalue Problems (submitted to SIAM J. Numer. Anal.) (1985).Google Scholar
  12. [12]
    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).CrossRefGoogle Scholar
  13. [13]
    W.C. Rheinboldt and J.V. Burkhardt, A locally parametrized Continuation Process, ACM Trans. Math. Software 9, 215–235 (1983).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • R. E. Bank
    • 1
  • H. D. Mittelmann
    • 2
  1. 1.Department of MathematicsUC San DiegoLa Jolla
  2. 2.Department of MathematicsArizona State UniversityTempe

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