An Improved KM Algorithm for Computing the Structural Index of DAE System

Modeling and simulation technology is widely used to design complex products in industry. The problem of solving DAEs(Differential Algebraic Equations) is a key part of modeling and simulation technology, and computing the structural index of DAEs correctly and efficiently is very important to solve DAEs. The traditional algebraic method to compute the structural index is very costly. In this paper, we firstly convert the problem of computing the structural index of DAEs into the maximum weighted matching problem of bipartite graph, reducing a mass of symbolic manipulations; and then, we present an improved KM algorithm(called as Greedy_KM in this paper) based on the properties of DAEs to solve this matching problem. In order to solve the matching problem efficiently, it firstly computes matches as much as possible using greedy strategy, and then call KM algorithm to search the matches for the unmatched vertices after the step of greedy strategy. This paper also gives a set of numerical experiments to evaluate the time performance of our method. The results show that the time performance of Greedy_KM algorithm is significantly improved compared with the traditional Gaussian elimination algorithm and classical KM algorithm.