Newton-GMRES Method for Coupled Nonlinear Systems Arising in Semiconductor Device Simulation

  • C. Simon
  • M. Sadkane
  • S. Mottet
Conference paper


We are interested in computing the solution of a system of coupled nonlinear PDE’s which describes the electrical behaviour of semiconductor devices. This set of nonlinear equations is solved via a nonlinear version of the GMRES method [2]. This method consists in solving the linear system, that arises in Newton’s method, by an iterative scheme, which constructs an orthonormal basis of a Krylov subspace, and minimizes the residual, over the current Krylov subspace. An advantage of this method over the classical ones is that the Jacobian is not stored and that little storage is required since the method restarts periodically whenever the size of the Krylov subspace reaches a maximum value fixed by the user.


Jacobian Matrix Semiconductor Optical Amplifier Krylov Subspace Rectangular Mesh GMRES Method 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. Saad and M. Schultz. GMRES: A Generalized Minimal Residual Algorithm for solving nonsymmetric linear systems. SIAM J. Sci. and Stat. Comp. Number 7. pp:856–869, 1986.MATHCrossRefGoogle Scholar
  2. [2]
    P. Brown and Y. Saad. Hybrid Krylov methods for solving nonlinear systems of equations. SISSC. vol.11,no.3,pp 450–481,1990.MathSciNetMATHGoogle Scholar
  3. [3]
    T. Kerhoven and Y. Saad. On acceleration methods for coupled nonlinear elliptic. Numer. Math.60,525–548 (1992).MathSciNetCrossRefGoogle Scholar
  4. [4]
    Z. Johan. Data parallel finite element techniques for large scale computational fluid dynamics. PhD Thesis. Stanford University. July 1992.Google Scholar
  5. [5]
    C. Simon, S. Mottet, J. E. Viallet. Autoadaptive Mesh Refinement. SISDEP91. Vol.4, pp225–233. W. Fichtner and D. Aemmer editors.Google Scholar
  6. [6]
    C. Simon, S. Mottet. FCBM: Flux Conservative Box Method, a new discretization strategy of the semiconductor equations, in preparation.Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • C. Simon
    • 1
    • 2
  • M. Sadkane
    • 2
  • S. Mottet
    • 1
  1. 1.CNET Lannion BFrance TelecomLannion CédexFrance
  2. 2.IRISA Campus de BeaulieuRennes CédexFrance

Personalised recommendations