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A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

Author

Listed:
  • Juan Tang

    (School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
    Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Yongsheng Rao

    (School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
    Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

Abstract

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications has emerged and became widely accepted; they generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAE systems with large dimensions, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on the Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameters has been presented. It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples, and preliminary numerical experiments show that the time complexity of BPA can be reduced by at least O ( ℓ ) compared to the MPA, which is mainly consistent with the results of our analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2057-:d:446837
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    References listed on IDEAS

    as
    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. 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.
    3. Atiyah Elsheikh & Wolfgang Wiechert, 2018. "The structural index of sensitivity equation systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 24(6), pages 573-592, November.
    Full references (including those not matched with items on IDEAS)

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