指标约简中Gear算法的实现

Realization of Gear method in index reduction

基于组件的建模有时会产生高指标的微分代数方程(DAE),不能直接求解,需要进行指标约简。Gear方法是一个经典的指标约简方法,对Gear方法从理论上进行了说明和分析。对于一类具有特殊结构的DAE,提出了Gear方法实现中的优化策略,以降低指标约简后得到的方程规模。把优化后的实现与未优化的实现进行了比对,实验结果表明,优化过的实现方法针对这类特殊的问题确实达到了更好的约简效果。

Component based modeling generates high index differential algebraic equation（DAE） sometimes,which can’t be solved directly,so index reduction is needed.Gear method is a classic index reduction method,it is introduced and analyzed theoretically.For one kind of DAE with special structure,optimization strategy in realization of Gear method is proposed to reduce the equations scale after index reduction.The optimized realization is compared with the general one by experiment and the result shows that the optimized realization has better reduction result on the special kind of problem.