Speaker: Guangning (Gary) Tan, McMaster University
Title: Conversion Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems
We present two conversion methods for improving the Sigma-method, which performs structural analysis (SA) of differential-algebraic equations (DAEs). This SA is used to determine the index of a DAE before a numerical solution method is applied. Equivalent to Pantelides's algorithm, our SA succeeds on many DAEs of practical interest, but can fail on simple, solvable ones with an identically singular Jacobian and thus incorrect structural information. Our conversion methods are aimed at overcoming such failures. They reformulate a DAE on which the Sigma-method fails into an equivalent problem on which our SA is more likely to produce a nonsingular Jacobian and hence succeed. We can automate the conversion process using a symbolic tool. We also show how to combine our methods with a block triangularization of DAEs. This approach improves the efficiency of finding a useful conversion for fixing SA's failures.