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

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.

Hierarchical Structural Analysis Method for Complex Equation-Oriented Models

“…It is equivalent to the algorithm by Pantelides for the index-1 DAEs. The last 20 years have seen several extension works on developing the signature matrix-based structural analysis methods [23][24][25][26][27] and related tools [28]. However, these approaches only find, but cannot diagnose, the ill-posed model, because they will terminate their execution if a structural deficiency is encountered.…”