Conversion Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems
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Differential-algebraic equation systems (DAEs) are generated routinely by simulation and modeling environments. Before a simulation starts and a numerical method is applied, some kind of structural analysis (SA) is used to determine which equations to be differentiated, and how many times. Both Pantelides's algorithm and Pryce's Σ-method are equivalent: if one of them finds correct structural information, the other does also. Nonsingularity of the Jacobian produced by SA indicates a success, which occurs on many problems of interest. However, these methods can fail on simple, solvable DAEs and give incorrect structural information including the index. This article investigates Σ-method's failures and presents two conversion methods for fixing them. Both methods convert a DAE on which the Σ-method fails to an equivalent problem on which this SA is more likely to succeed.
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