微分代数系统结构化分析

Structural analysis for differential algebraic systems

对工程和科学问题进行建模和仿真的时候,人们常常很自然地会用微分代数系统对这些问题进行描述.为了检验微分代数系统的初始相容性并进行求解,对微分代数系统进行结构化分析非常重要.本文对经典的微分代数系统结构化分析方法进行了深入的研究;提出了一种新的结构化分析方法,可以高效地对大规模、高阶高指标的微分代数系统进行结构化分析,并快速检验其初始相容性;证明了该方法的终止性,分析了其最坏时间复杂度.该方法的关键在于对最大加权二部子图的使用,而最大加权二部子图则来源于原始系统的加权二部图.实验结果显示,该方法能高效地完成对微分代数系统的结构化分析.

It is natural to describe physical system with differential algebraic system when modeling and simulating many engineering and scientific problems.Structural analysis is very important for the consistent initialization of differential algebraic system and finally solving it.In this paper,we research the classical methods for structural analysis of differential algebraic systems;and then we propose a new and more time efficient method for structural analysis of large scale differential algebraic systems that have a high index and a high order,and this method can quickly verifies the consistent initialization of the differential algebraic system,find out which equations and how many times they need differentiating as well;we prove the termination of this new method and analyze the worst time complexity of it.The key to this proposed method is the use of maximal weighted bipartite sub-graphs,which are derived from the base of weighted bipartite graphs of the original system.Demonstration and testing show that this method is effective and time efficient for structural analysis of differential algebraic systems.