组合松弛算法的研究与分析

Research and analysis of combinatorial relaxation algorithm

基于Modelica语言的仿真建模往往得到的数学模型是高指标的微分代数系统,结构指标约简算法是约简此类高指标问题的一种快速算法。为了解决算法少数情况下的失效问题,深入研究和分析了一种修正算法——组合松弛算法。针对线性时不变系统设计并实现了该算法,并通过两个具体实例表明了组合松弛算法能够有效地检测并修正结构指标约简算法的失效问题。

Modelica language based modeling and simulation usually gets a mathematical model which is a high-indexed differentialalgebraic equation system. The structural index reduction algorithms can serve as a fast method to reduce such high-indexed issues. In order to solve the failure of the structural index reduction algorithms in a few cases, another algorithm which is called combinatorial relaxation algorithm is analyzed and studied. Then, the algorithm is verified by a linear time-invariant system modeling process with two examples presented, respectively. Finally, the result of these two examples shows the correction algorithm presented is an effective way to detect and correct the application of structural index reduction algorithms.