Advertisement

Further Improvements in Nonsymmetric Hybrid Iterative Methods

  • H. A. Van der Vorst
  • D. R. Fokkema
  • G. L. Sleijpen

Abstract

In the past few years new methods have been proposed that can be seen as combinations of standard Krylov subspace methods, such as Bi—CG and GM-RES. Such hybrid schemes include CGS, BiCGSTAB, QMRS, TFQMR, and the nested GMRESR method. These methods have been successful in solving relevant sparse nonsymmetric linear systems, but there is still a need for further improvements. In this paper we will highlight some of the recent advancements in the search for effective iterative solvers.

Keywords

Iteration Count Matrix Entry Sparsity Pattern Incomplete Factor Short Channel Device 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Driessen, H.A.v.d. Vorst, Bi-CGSTAB in Semiconductor Modeling, Proc. SISDEP (1991).Google Scholar
  2. [2]
    O. Heinreichsberger et al., Fast Iterative Solution of Carrier Continuity Equations for Three-Dimensional Device Simulation,SIAM J.Sci.Stat.Comp., Vol. 13, No. 1, pp. 289–306 (1992).MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    C. Pommerell, Solution of Large Unsymmetric Systems of Linear Equations, Doctoral Thesis, ETH Zurich (1992).Google Scholar
  4. [4]
    Y. Saad, Preconditioning Techniques for Nonsymmetric and Indefinite Linear Systems, J.Comp. Appl.Math., Vol. 24, pp. 89–105 (1988).MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    S.M. Sze, High-Speed Semiconductor Devices, John Wiley & Sons, p. 177 (1990).Google Scholar
  6. [6]
    H.A.v.d. Vorst, A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Systems, SIAM J.Sci.Stat.Comp., Vol. 13, No. 2, pp. 631–644 (1992).MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • H. A. Van der Vorst
    • 1
  • D. R. Fokkema
    • 1
  • G. L. Sleijpen
    • 1
  1. 1.Mathematical InstituteUniversity of UtrechtUtrechtThe Netherlands

Personalised recommendations