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Numerical Experiments

  • Reijer Idema
  • Domenico J. P. Lahaye
Chapter
Part of the Atlantis Studies in Scientific Computing in Electromagnetics book series (ASSCE, volume 1)

Abstract

In this chapter, numerical experiments with the Newton-Krylov power flow solver are presented. This includes numerical experiments with LU and ILU factorisations, matrix ordering methods, and forcing term strategies, experiments with the power flow solver for all combinations of preconditioners and forcing terms, and experiments regarding contingency analysis.

Keywords

Power Flow Force Term Newton Iteration Fill Ratio Residual Norm 
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.

References

  1. 1.
    Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., Curfman McInnes, L., Smith, B.F., Zhang, H.: PETSc users manual. Tech. Rep. ANL-95/11 - Revision 3.1, Argonne National Laboratory (2010). http://www.mcs.anl.gov/petsc/
  2. 2.
    Duff, I.S., Erisman, A.M., Reid, J.K.: Direct Methods for Sparse Matrices. Oxford University Press, New York (1986)Google Scholar
  3. 3.
    Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)Google Scholar
  4. 4.
    Amestoy, P.R., Davis, T.A., Duff, I.S.: An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17(4), 886–905 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Davis, T.A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 165–195 (2004)CrossRefzbMATHGoogle Scholar
  6. 6.
    Amestoy, P.R., Duff, I.S., L’Excellent, J.Y., Koster, J.: A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23(1), 15–41 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Demmel, J.W., Eisenstat, S.C., Gilbert, J.R., Li, X.S., Liu, J.W.H.: A supernodal approach to sparse partial pivoting. SIAM J. Matrix Anal. Appl. 20(3), 720–755 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Li, X.S., Demmel, J.W.: SuperLU\_DIST: a scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Trans. Math. Softw. 29(2), 110–140 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Dembo, R.S., Steihaug, T.: Truncated-Newton algorithms for large-scale unconstrained optimization. Math. Prog. 26, 190–212 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Eisenstat, S.C., Walker, H.F.: Choosing the forcing terms in an inexact Newton method. SIAM J. Sci. Comput. 17(1), 16–32 (1996)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Atlantis Press and the authors 2014

Authors and Affiliations

  1. 1.Numerical AnalysisDelft University of TechnologyDelftThe Netherlands

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