Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation
Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation
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DOI：
10.1007/s10107-008-0227-8
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发表时间：
2010
影响因子：
2.7
通讯作者：
S. Iwata;Mizuyo Takamatsu
中科院分区：
文献类型：
--
作者：
S. Iwata;Mizuyo Takamatsu
电路分析的现代建模方法导致微分代数方程（DAE）。DAE的索引是数字难度的度量。一般来说，指数越高，求解DAE的难度越大。由修正节点分析（MNA）产生的DAE的指数由电路的结构唯一地确定。相反，我们考虑一类更广泛的分析方法，称为混合分析。对于线性时不变电路，我们设计了一个组合算法，以找到一个最佳的混合分析，其中要解决的DAE的指数达到最小值。最优混合分析通常会导致DAE的索引低于MNA。
Modern modeling approaches for circuit analysis lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. The index of the DAE arising from the modified nodal analysis (MNA) is determined uniquely by the structure of the circuit. Instead, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant electric circuits, we devise a combinatorial algorithm for finding an optimal hybrid analysis in which the index of the DAE to be solved attains the minimum. The optimal hybrid analysis often results in a DAE with lower index than MNA.