%0 Journal Article %1 Sielemann20112673 %A Sielemann, M. %A Schmitz, G. %D 2011 %J Mathematics and Computers in Simulation %K 2011 Modelica initialization mathematics simulation %N 12 %P 2673 - 2687 %R 10.1016/j.matcom.2011.05.010 %T A quantitative metric for robustness of nonlinear algebraic equation solvers %U http://dx.doi.org/10.1016/j.matcom.2011.05.010 %V 81 %X 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.

@article{Sielemann20112673, 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. }, added-at = {2013-09-09T16:15:54.000+0200}, author = {Sielemann, M. and Schmitz, G.}, biburl = {https://www.bibsonomy.org/bibtex/20716dbe8a27281db7f6e864cd03e6563/thorade}, description = {A quantitative metric for robustness of nonlinear algebraic equation solvers}, doi = {10.1016/j.matcom.2011.05.010}, interhash = {ac5bdf4c9b084c7cf0e143119274b51c}, intrahash = {0716dbe8a27281db7f6e864cd03e6563}, issn = {0378-4754}, journal = {Mathematics and Computers in Simulation }, keywords = {2011 Modelica initialization mathematics simulation}, number = 12, pages = {2673 - 2687}, timestamp = {2013-09-09T16:15:54.000+0200}, title = {A quantitative metric for robustness of nonlinear algebraic equation solvers }, url = {http://dx.doi.org/10.1016/j.matcom.2011.05.010}, volume = 81, year = 2011 }