Conversion Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems
For users of simulation environments, this work addresses a known failure mode of structural analysis on DAEs, but the solution is incremental, building on existing methods.
The paper investigates failures of structural analysis methods (Pantelides's algorithm and Pryce's Σ-method) on solvable differential-algebraic equation systems (DAEs) and proposes two conversion methods that transform failing DAEs into equivalent forms where structural analysis succeeds.
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.