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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
DOI: https://doi.org/10.1090/S0025-5718-2011-02558-5
Published electronically: November 8, 2011
MathSciNet review: 2869043
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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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Additional Information

Satoru Iwata
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: iwata@kurims.kyoto-u.ac.jp

Mizuyo Takamatsu
Affiliation: Department of Information and System Engineering, Chuo University, Tokyo 112-8551, Japan
Email: takamatsu@ise.chuo-u.ac.jp

Caren Tischendorf
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Köln, Germany
Email: tischendorf@math.uni-koeln.de

DOI: https://doi.org/10.1090/S0025-5718-2011-02558-5
Keywords: Differential-algebraic equations, index, circuit simulation, hybrid analysis
Received by editor(s): May 18, 2010
Received by editor(s) in revised form: February 23, 2011
Published electronically: November 8, 2011
Additional Notes: The first author was supported by a Grant-in-Aid for Scientific Research from the Japan Society for Promotion of Science.
The second author was supported by a Grant-in-Aid for Scientific Research from the Japan Society for Promotion of Science.
The third author was supported by the European Union within the framework of the project “Integrated Circuit/EM Simulation and design Technologies for Advanced Radio Systems-on-chip” (FP7/2008/ICT/214911).
Article copyright: © Copyright 2011 American Mathematical Society