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Order Reduction of General Nonlinear DAE Systems by Automatic Tearing

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  • Emanuele Carpanzano

Abstract

The object-oriented approach to modelling has recently made possible to build models of large-scale real systems. However, the resulting system of equations is generally a nonlinear DAE (Differential Algebraic Equations) system of large dimension, which must be reduced in some way to make it tractable for numerical solutions. A way to do this is automatic symbolic tearing, which aims at splitting the DAE system into two parts: a core consisting of a reduced implicit DAE system and a set of explicit assignments. The problem is here dealt with by a graph theoretic approach, first proving the NP-completeness in the general case, then formulating the problem with reference to a bipartite graph and finally defining an efficient and flexible algorithm for automatic tearing. It is also shown how the proposed algorithm can easily incorporate both general and domain-specific heuristic rules, and can also be used to deal with equations in vector form. The application to serial multibody systems is considered as a significant example.

Suggested Citation

  • Emanuele Carpanzano, 2000. "Order Reduction of General Nonlinear DAE Systems by Automatic Tearing," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 6(2), pages 145-168, June.
    • Handle: RePEc:taf:nmcmxx:v:6:y:2000:i:2:p:145-168
    DOI: 10.1076/1387-3954(200006)6:2;1-M;FT145
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    Cited by:

    1. Casella, Francesco & Bachmann, Bernhard, 2021. "On the choice of initial guesses for the Newton-Raphson algorithm," Applied Mathematics and Computation, Elsevier, vol. 398(C).

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