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Efficient index reduction algorithm for large scale systems of differential algebraic equations

Author

Listed:
  • Qin, Xiaolin
  • Tang, Juan
  • Feng, Yong
  • Bachmann, Bernhard
  • Fritzson, Peter

Abstract

In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature of DAEs is a sparse large scale system of fully nonlinear and high index. To make use of its sparsity, this paper provides a simple and efficient algorithm for index reduction of large scale DAEs system. We exploit the shortest augmenting path algorithm for finding maximum value transversal (MVT) as well as block triangular forms (BTFs). We also present the extended signature matrix method with the block fixed point iteration and its complexity results. Furthermore, a range of nontrivial problems are demonstrated by our algorithm.

Suggested Citation

  • Qin, Xiaolin & Tang, Juan & Feng, Yong & Bachmann, Bernhard & Fritzson, Peter, 2016. "Efficient index reduction algorithm for large scale systems of differential algebraic equations," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 10-22.
    • Handle: RePEc:eee:apmaco:v:277:y:2016:i:c:p:10-22
    DOI: 10.1016/j.amc.2015.11.091
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    References listed on IDEAS

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    1. Carpanzano, Emanuele & Maffezzoni, Claudio, 1998. "Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(2), pages 133-150.
    2. M. L. Balinski, 1985. "Signature Methods for the Assignment Problem," Operations Research, INFORMS, vol. 33(3), pages 527-536, June.
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    Cited by:

    1. Qin, Xiaolin & Yang, Lu & Feng, Yong & Bachmann, Bernhard & Fritzson, Peter, 2018. "Index reduction of differential algebraic equations by differential Dixon resultant," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 189-202.
    2. Marzorati, Denise & Fernández, Joaquin & Kofman, Ernesto, 2022. "Efficient connection processing in equation–based object–oriented models," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    3. Juan Tang & Yongsheng Rao, 2020. "A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations," Mathematics, MDPI, vol. 8(11), pages 1-15, November.

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