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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Tractability index of hybrid equations for circuit simulation
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by Satoru Iwata, Mizuyo Takamatsu and Caren Tischendorf PDF
Math. Comp. 81 (2012), 923-939 Request permission

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
  • MR Author ID: 346469
  • Email: tischendorf@math.uni-koeln.de
  • 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).
  • © Copyright 2011 American Mathematical Society
  • 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
  • MathSciNet review: 2869043