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BIT Numerical Mathematics

, Volume 56, Issue 1, pp 319–340 | Cite as

Regularization of DAEs based on the Signature method

  • Lena ScholzEmail author
  • Andreas Steinbrecher
Article

Abstract

Automated modeling of multi-physics dynamical systems often results in large-scale high-index differential-algebraic equations (DAEs). Since direct numerical simulation of such systems leads to instabilities and possibly non-convergence of numerical methods, a regularization or remodeling is required. In many simulation environments, a structural analysis based on the sparsity pattern of the system is used to determine the index and an index-reduced system model. Here, usually the Pantelides algorithm in combination with the Dummy Derivative Method is used. We present a new approach for the regularization of DAEs that is based on the Signature method (\(\varSigma \)-method).

Keywords

Differential-algebraic equation Regularization Structural analysis \(\varSigma \)-method Index reduction 

Mathematics Subject Classification

65L80 34A09 37M05 

Notes

Acknowledgments

We would like to thank two anonymous referees for their careful reading and for thoughtful suggestions for the improvement of the paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für MathematikBerlinFederal Republic of Germany

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