### 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 language | English |
---|---|

Pages (from-to) | 72-87 |

Number of pages | 16 |

Journal | Applied Numerical Mathematics |

Volume | 103 |

DOIs | |

Publication status | Published - 1 May 2016 |

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### Keywords

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

### Cite this

*Applied Numerical Mathematics*,

*103*, 72-87. https://doi.org/10.1016/j.apnum.2016.01.002

}

*Applied Numerical Mathematics*, vol. 103, pp. 72-87. https://doi.org/10.1016/j.apnum.2016.01.002

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

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Model order reduction using singularly perturbed systems

AU - Mohaghegh, K.

AU - Pulch, R.

AU - Ter Maten, J.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

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.

KW - Differential algebraic equations

KW - Direct approach

KW - Linear model order reduction

KW - Parametric model reduction

KW - Semi-explicit systems

KW - ε-Embedding

UR - http://www.scopus.com/inward/record.url?scp=84956984488&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2016.01.002

DO - 10.1016/j.apnum.2016.01.002

M3 - Article

AN - SCOPUS:84956984488

VL - 103

SP - 72

EP - 87

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -