Structure-Preserving Model Order Reduction of RCL Circuit Equations

Freund, Robert M.

doi:10.1007/978-3-540-78841-6_3

Cited by 30 publications

(29 citation statements)

References 27 publications

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“…. , x K } a subspace S r ⊂ R n of dimension r is searched for that minimizes 16) where ρ r : R n → S r is the orthogonal projection onto S r . We will not describe POD in full detail here, as in literature, e. g., [1,38], this is well explained.…”

Section: Pod Methodsmentioning

confidence: 99%

“…Then a normal initial-value problem for the linear DAE (3.3a) has none or infinitely many solutions. The regularity of the matrix pencil can be checked by examining the element related incidence matrices [16].…”

Section: Chapter 3 Authorgroupmentioning

confidence: 99%

“…The concept of all projection based MOR techniques is to approximate the high dimensional state space vector x(t) ∈ R n with the help of a vector z(t) ∈ R r of reduced dimension r ≪ n, within the meaning of 16 Chapter 3 Authorgroup x(t) ≈x(t) := Vz(t) with V ∈ R n×r .…”

Section: Projection Based Mormentioning

confidence: 99%

“…Freund [13][14][15][16][17] developed a Krylov-based method where passivity, the structure and reciprocity are preserved. SPRIM (Structure-Preserving Reduced-Order Interconnect Macromodell) is similar to PRIMA as first the Arnoldi-method is run to create a matrix V ∈ R n×r .…”

Section: Structure Preservationmentioning

confidence: 99%

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Model Order Reduction: Methods, Concepts and Properties

Antoulas

Ionutiu

Martins

et al. 2015

Mathematics in Industry

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Model order reduction : methods, concepts and propertiesAntoulas, A.C.; Ionutiu, R.; Martins, N.; ter Maten, E.J.W.; Mohaghegh, K.; Pulch, R.; Rommes, J.; Saadvandi, M.; Striebel, M.Published: 01/01/2015 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):Antoulas, A. C., Ionutiu, R., Martins, N., Maten, ter, E. J. W., Mohaghegh, K., Pulch, R., ... Striebel, M. (2015). Model order reduction : methods, concepts and properties. (CASA-report; Vol. 1507). 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. Here eigenvalues are the starting point. The eigenvalue problems related to large-scale dynamical systems are usually too large to be solved completely. The algorithms described in this section are efficient and effective methods for the computation of a few specific dominant eigenvalues of these large-scale systems. It is shown how these algorithms can be used for computing reduced-order models with modal approximation and Krylov-based methods. Section 3.3, written by Maryam Saadvandi and Joost Rommes, concerns passivity preserving model order reduction using the spectral zero method. It detailedly discusses two algorithms, one by Antoulas and one by Sorenson. These two approaches are based on a projection method by selecting spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros. The reduced model preserves passivity. Section 3.4, written by Roxana Ionutiu, Joost Rommes and Athanasios C. Antoulas, refines the spectra...

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Section: Pod Methodsmentioning

confidence: 99%

Section: Chapter 3 Authorgroupmentioning

confidence: 99%

Section: Projection Based Mormentioning

confidence: 99%

Section: Structure Preservationmentioning

confidence: 99%

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Model Order Reduction: Methods, Concepts and Properties

Antoulas

Ionutiu

Martins

et al. 2015

Mathematics in Industry

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“…It connects to many other topics in realization theory, like controllability and observability properties, similarity invariants, balanced realizations and model reduction. Recently, additional properties, like structure preservation, for obtaining a minimal realization or an approximate reduced order model have received interest, e.g., [1], [5], [10]. Here, we take an analysis and control perspective, which motivates our interest in obtaining a minimal representation of a non-minimal portHamiltonian (PH) system that preserves the PH structure.…”

Section: Introductionmentioning

confidence: 99%

A structure preserving minimal representation of a nonlinear port-Hamiltonian system

Scherpen

Schaft

2008

2008 47th IEEE Conference on Decision and Control

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CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If 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.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Abstract-In this paper an approach to reduce nonlinear non-observable and non-strongly accessible port-Hamiltonian systems to an observable and strongly accessible portHamiltonian system, respectively, is treated. A local state decomposition (the nonlinear version of the Kalman decomposition) is instrumental for the approach that preserves the port-Hamiltonian structure. The strongly accessible reduction scheme goes along similar lines as the linear scheme. However, the observable reduction scheme is somewhat more involved. Under some additional assumptions, the reduction can be performed along the lines of the linear scheme. If these assumptions are not fulfilled, a reduction scheme for a zero-observable representation using duality in the co-energy coordinates is developed. Finally, the possibilities to apply the approaches of this paper to approximate order reduction by e.g., use of balancing procedures, is discussed.

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Model order reduction of nonlinear circuit equations

Steinbrecher

Stykel

2012

Circuit Theory & Apps

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SUMMARY In this paper, we present a model order reduction approach for nonlinear circuit equations with a small number of nonlinear elements. This approach is based on the decoupling of linear and nonlinear subcircuits and reducing the linear part using balancing‐related model reduction techniques. The efficiency and applicability of the proposed model reduction approach is demonstrated on numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.

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Structure-Preserving Model Order Reduction of RCL Circuit Equations

Cited by 30 publications

References 27 publications

Model Order Reduction: Methods, Concepts and Properties

Model Order Reduction: Methods, Concepts and Properties

A structure preserving minimal representation of a nonlinear port-Hamiltonian system

Model order reduction of nonlinear circuit equations

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