Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Tractability index of hybrid equations for circuit simulation

Authors: Satoru Iwata, Mizuyo Takamatsu and Caren Tischendorf
Journal: Math. Comp. 81 (2012), 923-939
MSC (2010): Primary 34A09, 94C05; Secondary 65L80, 94C15
Posted: November 8, 2011
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Abstract | References | Similar Articles | Additional Information

Abstract: Modern modeling approaches for circuit simulation such as the modified nodal analysis (MNA) 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.

In this paper, we consider a broader class of analysis methods called the hybrid analysis. For nonlinear time-varying circuits with general dependent sources, we give a structural characterization of the tractability index of DAEs arising from the hybrid analysis. This enables us to determine the tractability index efficiently, which helps to avoid solving higher index DAEs in circuit simulation.

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