Original article: A quantitative metric for robustness of nonlinear algebraic equation solvers

Authors:
M. Sielemann;G. Schmitz
Affiliations:
Deutsches Zentrum für Luft- und Raumfahrt, Institute of Robotics and Mechatronics, Department of System Dynamics and Control, Münchner Strasse 20, 82234 Wessling, Germany;Technische Universität Hamburg-Harburg, Institute of Thermo-Fluid Dynamics, Denickestr. 17, 21073 Hamburg, Germany
Venue:
Mathematics and Computers in Simulation
Year:
2011

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Abstract

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.