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Regularization of DAEs based on the Signature method

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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).

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Notes

  1. The term structurally singular is also used slightly differently in the literature: on the one hand, it is used for systems that do not allow an assignment of the highest occurring derivative of each variables to a specific equation (i.e., systems that do not have a transversal with finite value) [18], and on the other hand it is used for systems with singular \(\varSigma \)-Jacobian [16].

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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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Authors and Affiliations

  1. Institut für Mathematik, Ma 4-5, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Federal Republic of Germany

    Lena Scholz & Andreas Steinbrecher

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  1. Lena Scholz
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  2. Andreas Steinbrecher
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Correspondence to Lena Scholz.

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Communicated by Hans-Petter Langtangen.

Research supported by European Research Council, through ERC Advanced Grant MODSIMCONMP.

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Scholz, L., Steinbrecher, A. Regularization of DAEs based on the Signature method. Bit Numer Math 56, 319–340 (2016). https://doi.org/10.1007/s10543-015-0565-x

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