BIT Numerical Mathematics

, Volume 56, Issue 2, pp 777–804 | Cite as

Structural-algebraic regularization for coupled systems of DAEs

  • Lena ScholzEmail author
  • Andreas Steinbrecher


In the automated modeling of multi-physics dynamical systems, frequently different subsystems are coupled together via interface or coupling conditions. This approach often results in large-scale high-index differential-algebraic equations (DAEs). Since the direct numerical simulation of these kinds of systems leads to instabilities and possibly non-convergence of numerical methods, a regularization or remodeling of such systems is required. In many simulation environments, a structural method that analyzes the system based on its sparsity pattern is used to determine the index and an index-reduced system model. However, this approach is not reliable for certain problem classes, and in particular not suited for coupled systems of DAEs. We present a new approach for the regularization of coupled dynamical systems that combines the Signature method (\({\varSigma }\)-method) for the structural analysis with algebraic regularization techniques. This allows to handle structurally singular systems and also enables a proper treatment of redundancies or inconsistencies in the system.


Differential-algebraic equation Coupled system Regularization Structural analysis \({\varSigma }\)-method Structurally singular 

Mathematics Subject Classification

65L80 34A09 37M05 



We would like to thank two anonymous referees for their careful reading and for thoughtful suggestions for the improvement of the paper. We also thank Jakob Schneck for performing the computations and comparisons of the different simulation environments.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für Mathematik, Ma 4-5TU BerlinBerlinFederal Republic of Germany

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