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Model order reduction using singularly perturbed systems

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  • NETL
  • NSTL
  • Elsevier
Nowadays electronic circuits comprise about a hundred million components on slightly more than one square centimeter. The model order reduction (MOR) techniques are among the most powerful tools to conquer this complexity and scale, although the nonlinear MOR is still an open field of research. On the one hand, the MOR techniques are well developed for linear ordinary differential equations (ODEs). On the other hand, we deal with differential algebraic equations (DAEs), which result from models based on network approaches. There are the direct and the indirect strategy to convert a DAE into an ODE. We apply the direct approach, where an artificial parameter is introduced in the linear system of DAEs. This results in a singular perturbed problem. On compact domains, uniform convergence of the transfer function of the regularized system towards the transfer function of the system of DAEs is proved in the general linear case. This convergence is for the transfer functions of the full model. We apply and investigate two different ways of MOR techniques in this context We have two test examples, which are both TL models.

Differential algebraic equationsSemi-explicit systemsDirect approachε-EmbeddingLinear model order reductionParametric model reduction

Kasra Mohaghegh、Roland Pulch、Jan ter Maten

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Depto. Ingenieria Mecanica, Aragon Institute of Engineering Research (I3A), Universidad de Zaragoza, Maria de Luna s/n, Campus Rio Ebro, Edificio 'Agustin de Betancourt', 50018 Zaragoza, Spain

Institut fuer Mathematik und Informatik, Walther-Rathenau-Strasse 47, D-17487 Greifswald, Germany

Lehrstuhl fuer Angewandte Mathematik und Numerische Mathematik, Fachbereich Mathematik und Naturwissenschaften, Bergische Universitaet Wuppertal Gaussstr. 20, D-42119 Wuppertal, Germany,Department for Mathematics and Computer Science, CASA, Eindhoven University of Technology, P.O. Box 513,5600 MB Eindhoven, The Netherlands

2016

10.1016/j.apnum.2016.01.002

Applied numerical mathematics: Transactions of IMACS

Applied numerical mathematics: Transactions of IMACS

ISSN：0168-9274
年,卷(期)：2016.103(May)
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