Multi-parameter polynomial order reduction of linear finite element models

Farle, Ortwin; Hill, V.; Ingelström, Pär; Dyczij‐Edlinger, Romanus

doi:10.1080/13873950701844220

Cited by 28 publications

(19 citation statements)

References 24 publications

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“…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%

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: Moment-matchingmentioning

confidence: 99%

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

2015

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“…Further use of moment-matching approaches is taken into account in commercial software [48]. Notorious extension to multi-parameter configurations of these techniques is addressed in [14,13], where not only a frequency sweep is carried out but also dielectric properties of different materials are swept. On the other hand, there is an increasing interest in SVD approaches.…”

Section: Introductionmentioning

confidence: 99%

Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

Rubia

Razafison

Maday

2009

IEEE Trans. Microwave Theory Techn.

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In this paper, a reduced basis approximation-based model order reduction for fast and reliable frequency sweep in the time-harmonic Maxwell's equations is detailed. Contrary to what one may expect by observing the frequency response of different microwave circuits, the electromagnetic field within these devices does not drastically vary as frequency changes in a band of interest. Thus, instead of using computationally inefficient, large dimension, numerical approximations such as finite element or boundary element methods for each frequency in the band, the point in here is to approximate the dynamics of the electromagnetic field itself as frequency changes. A much lower dimension, reduced basis approximation sorts this problem out. Not only rapid frequency evaluation of the reduced order model is carried out within this approach, but also special emphasis is placed on a fast determination of the error measure for each frequency in the band of interest. This certifies the accurate response of the reduced order model. The same scheme allows us, in an offline stage, to adaptively select the basis functions in the reduced basis approximation and automatically select the model order reduction process whenever a preestablished accuracy is required throughout the band of interest. Finally, real-life applications will illustrate the capabilities of this approach.

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“…Several approaches have been proposed for the PMOR problem. The authors of [12,17,21,23,34] proposed to match the so-called generalized moments of the transfer function H(p, s) through projecting the original system on (the union of) generalized Krylov subspaces. A closely related interpolatory H 2 -optimal model reduction method for parameterized systems was considered in [8,11].…”

Section: Is Reciprocal If H(s) = Sh(s)mentioning

confidence: 99%