Parameter independent model order reduction

Feng, Lihong

doi:10.1016/j.matcom.2004.12.002

Cited by 32 publications

(30 citation statements)

References 14 publications

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“…This enables rapid characterization of the aircraft's flight envelope, calculations that would otherwise require many weeks of computation time. Parametric reduced models have also shown to be an important enabling technology in the synthesis and design of interconnect [55,71], semiconductor devices [130], and MEMS [31,91] as well as in electrochemical [95] and electrothermal applications [96].…”

Section: Applications Of Parametric Model Reductionmentioning

confidence: 99%

“…This has been discussed in numerous publications in the past two decades, e.g., [93,96,119,153,222] for the single parameter case, [83] for a special two-parameter case arising in structural dynamics, [89,91,150] for linear and polynomial parametric dependence, and [71,120,164,176] for more general parametric dependence but only in some of the state-space matrices. Moment-matching/interpolation properties can be proved (see, e.g., [43,71,93,120,222]) analogously as for standard moment-matching methods such as Padé-via-Lanczos [90,103].…”

Section: Moment-matchingmentioning

confidence: 99%

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A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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Section: Applications Of Parametric Model Reductionmentioning

confidence: 99%

Section: Moment-matchingmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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“…A general projection framework for structure-preserving PMOR can be described as follows: suppose that (constant) matrices V r , W r ∈ C n×r are specified with r n and rank(V r ) = rank(W r ) = r and define an associated reduced system (see, e.g., [18,12,17,27,49]): …”

Section: 1) E(p)ẋ(t) = A(p) X(t) + B(p) U(t) Y(t) = C(p) X(t)mentioning

confidence: 99%

Interpolatory Projection Methods for Parameterized Model Reduction

Baur¹,

Beattie²,

Benner³

et al. 2011

SIAM J. Sci. Comput.

198

195

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Abstract. We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model. Moreover, we are able to give conditions under which the gradient and Hessian of the system response with respect to the system parameters is matched in the reduced-order model. We provide a systematic approach built on established interpolatory H 2 optimal model reduction methods that will produce parameterized reduced-order models having high fidelity throughout a parameter range of interest. For single input/single output systems with parameters in the input/output maps, we provide reduced-order models that are optimal with respect to an H 2 ⊗ L 2 joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications. 1. Introduction. Numerical simulation has steadily increased in importance across virtually all scientific and engineering disciplines. In many application areas, experiments have been largely replaced by numerical simulation in order to save costs in design and development. High accuracy simulation requires high fidelity mathematical models which in turn induce dynamical systems of very large dimension. The ensuing demands on computational resources can be overwhelming and efficient model utilization becomes a necessity. It often is both possible and prudent to produce a lower dimension model that approximates the response of the original one to high accuracy. There are many model reduction strategies in use that are remarkably effective in the creation of compact, efficient, and high fidelity dynamical system models. Such a reduced model can then be used reliably as an efficient surrogate to the original system, replacing it as a component in larger simulations, for example, or in allied contexts that involve design optimization or the development of low-order, fast controllers suitable for real time applications.Typically, a reduced-order model will represent a specific instance of the physical system under study and as a consequence will have high fidelity only for small variations around that base system instance. Significant modifications to the physical model such as geometric variations, changes in material properties, or alterations in

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“…In several tests we made, this first term indeed was much smaller than the other term. Note that we not intend to solve (4.159) by using a fixed projection matrix V, valid for p = p 0 , for several different values of p. The danger of obtaining improper results when doing this was pointed out by [83]. Contrarily, we always apply an up-to-date matrix V(p).…”

Section: The Bram Algorithmmentioning

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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Parameter independent model order reduction

Cited by 32 publications

References 14 publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Interpolatory Projection Methods for Parameterized Model Reduction

Parameterized Model Order Reduction

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