Mathematical Programming

, Volume 121, Issue 1, pp 105–121

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

Authors

  • Satoru Iwata
    • Research Institute for Mathematical SciencesKyoto University
    • Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of Tokyo
FULL LENGTH PAPER Series A

DOI: 10.1007/s10107-008-0227-8

Cite this article as:
Iwata, S. & Takamatsu, M. Math. Program. (2010) 121: 105. doi:10.1007/s10107-008-0227-8

Abstract

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.

Keywords

Circuit simulationDAEIndexMatrix pencil

Mathematics Subject Classification (2000)

15A2234A0965L8068Q25

Copyright information

© Springer-Verlag 2008