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A quantitative metric for robustness of nonlinear algebraic equation solvers

Author

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  • Sielemann, M.
  • Schmitz, G.

Abstract

Practitioners in the area of dynamic simulation of technical systems report difficulties at times with steady-state initialization of models developed using general declarative modeling languages. These difficulties are analyzed in detail in this work and a rigorous approach to quantify robustness in the context of nonlinear algebraic equation systems is presented. This tool is then utilized in a study of six state of the art gradient-based iterative solvers on a set of industrial test problems. Finally, conclusions are drawn on the observed solver robustness in general, and it is argued whether the reported difficulties with steady-state initialization can be supported using the proposed quantitative metric.

Suggested Citation

  • Sielemann, M. & Schmitz, G., 2011. "A quantitative metric for robustness of nonlinear algebraic equation solvers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(12), pages 2673-2687.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:12:p:2673-2687
    DOI: 10.1016/j.matcom.2011.05.010
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