Model order reduction using singularly perturbed systems

K. Mohaghegh, R. Pulch, J. Ter Maten

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Abstract

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.

Original languageEnglish
Pages (from-to)72-87
Number of pages16
JournalApplied Numerical Mathematics
Volume103
DOIs
Publication statusPublished - 1 May 2016

Fingerprint

Model Order Reduction
Singularly Perturbed Systems
Algebraic Differential Equations
Transfer Function
Differential equations
Transfer functions
Linear Ordinary Differential Equations
Ordinary differential equations
Uniform convergence
Convert
Nonlinear Model
Ordinary differential equation
Linear Systems
Electronics
Model-based
Linear systems
Model
Networks (circuits)

Keywords

  • Differential algebraic equations
  • Direct approach
  • Linear model order reduction
  • Parametric model reduction
  • Semi-explicit systems
  • ε-Embedding

Cite this

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Model order reduction using singularly perturbed systems. / Mohaghegh, K.; Pulch, R.; Ter Maten, J.

In: Applied Numerical Mathematics, Vol. 103, 01.05.2016, p. 72-87.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Pulch, R.

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AB - 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.

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