Model order reduction using singularly perturbed systems

Mohaghegh, Kasra; Pulch, Roland; Maten, Jan ter

doi:10.1016/j.apnum.2016.01.002

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…Here we do not need to predefine the value of the ε. We obtain a parameterized MOR that gives a reduced model for ε = 0 for which the transfer function approximates well the one for the DAE [132,133].…”

Section: Discussionmentioning

confidence: 99%

Parameterized Model Order Reduction

Ciuprina

Villena

Dumitrache

et al. 2015

Mathematics in Industry

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Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA):Ciuprina, G., Fernández Villena, J., Ioan, D., Ilievski, Z., Kula, S., Maten, ter, E. J. W., ... Striebel, M. (2015). Parameterized model order reduction. (CASA-report; Vol. 1508). Eindhoven: Technische Universiteit Eindhoven. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract This Chapter introduces parameterized, or parametric, Model Order Reduction (pMOR). The Sections are offered in a prefered order for reading, but can be read independently. Section 4.1, written by Jorge Fernández Villena, L. Miguel Silveira, Wil H.A. Schilders, Gabriela Ciuprina, Daniel Ioan and Sebastian Kula, overviews the basic principles for pMOR. Due to higher integration and increasing frequency-based effects, large, full Electromagnetic Models (EM) are needed for accurate prediction of the real behavior of integrated passives and interconnects. Furthermore, these structures are subject to parametric effects due to small variations of the geometric and physical properties of the inherent materials and manufacturing process. Accuracy requirements lead to huge models, which are expensive to simulate and this cost is increased when parameters and their effects are taken into account. This Section introduces the framework of pMOR, which aims at generating reduced models for systems depending on a set of parameters. Section 4.2, written by Gabriela Ciuprina, Alexandra Ş tefȃnescu, Sebastian Kula and Daniel Ioan, provides robust procedures for pMOR. This Section proposes a robust specialized technique to extrac...

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Section: Discussionmentioning

confidence: 99%

Parameterized Model Order Reduction

Ciuprina

Villena

Dumitrache

et al. 2015

Mathematics in Industry

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“…In [23], a system of DAEs was regularised straightforward under the assumption of semi-explicit systems. Alternatively, we apply an approach for general descriptor systems from [26], which goes back to [39].…”

Section: Regularisationmentioning

confidence: 99%

Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction

Pulch

2019

International Journal of Control

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We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although the original system is asymptotically stable. We consider projection-based model order reduction of Galerkintype. A transformation of the original system ensures that any reduced system is asymptotically stable. This transformation requires the solution of a high-dimensional Lyapunov inequality. We solve this problem using a specific Lyapunov equation. Its solution can be represented as a matrix-valued integral in the frequency domain. Consequently, quadrature rules yield numerical approximations, where large sparse linear systems of algebraic equations have to be solved. We analyse this approach and show a sufficient condition on the error to meet the Lyapunov inequality. Furthermore, this technique is extended to systems of differential-algebraic equations with strictly proper transfer functions by a regularisation. Finally, we present results of numerical computations for high-dimensional examples, which indicate the efficiency of this stability-preserving method.

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“…In [134] it was shown that spectral zeros are solved efficiently from an associated Hamiltonian eigenvalue problem [127,137]. In [114,134] however, the selection of spectral zeros was still an open problem.…”

Section: Dominant Spectral Zeros and Implementationmentioning

confidence: 99%

“…The following pseudocode is extracted from [130, Chapter 3] and [131], with efficient modifications to automatically account for the four-fold symmetry ( ; ; ; ) of spectral zeros. Rather, due to the structure of the Hamiltonian matrices [127,137], they can be written down directly from the already converged left/right eigenvectors for , as shown in steps 14-17 of Algorithm 4.9. It turns out that the right/left eigenvectors corresponding to need not be solved for explicitly.…”

Section: Appendix: Sadpa For Computing Dominant Spectral Zerosmentioning

confidence: 99%