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Index characterization of differential-algebraic equations in hybrid analysis for circuit simulation

机译:电路仿真混合分析中微分-代数方程的指标表征

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Modern modeling approaches in circuit simulation naturally 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, the more difficult it is to solve the DAE. The modified nodal analysis (MNA) is known to yield a DAE with index at most two in a wide class of nonlinear time-varying electric circuits.rnIn this paper, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant RLC circuits, we prove that the index of the DAE arising from the hybrid analysis is at most one, and give a structural characterization for the index of a DAE in the hybrid analysis. This yields an efficient algorithm for finding an optimal hybrid analysis in which the index of the DAE to be solved attains zero. Finally, for linear time-invariant electric circuits that may contain dependent sources, we prove that the optimal hybrid analysis by no means results in a higher index DAE than MNA.
机译:电路仿真中的现代建模方法自然会导致微分代数方程(DAE)。 DAE的指数是数字难度程度的度量。通常,指数越高,解决DAE的难度就越大。在广泛的非线性时变电路中,改进的节点分析(MNA)可以产生DAE,其索引最多为2。在本文中,我们考虑了一种更广泛的分析方法,称为混合分析。对于线性时不变RLC电路,我们证明了混合分析产生的DAE的索引最大为1,并给出了混合分析中DAE的索引的结构表征。这产生了一种用于找到最佳混合分析的有效算法,在该算法中,要求解的DAE的索引变为零。最后,对于可能包含依赖源的线性时不变电路,我们证明最佳混合分析决不会导致比MNA更高的DAE指数。

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