Preserving the film coefficient as a parameter in the compact thermal model for fast electrothermal simulation

Feng, Lihong; Rudnyi, Evgenii B.; Korvink, Jan G.

doi:10.1109/tcad.2005.852660

Cited by 51 publications

(45 citation statements)

References 23 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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“…Multi-moment matching PMOR methods can be found in [11,16,18,19,44,45]. All these methods are based on Galerkin projection, i.e.…”

Section: Review Of Multi-moment Matching Pmor Methodsmentioning

confidence: 99%

“…We propose several a posteriori error bounds for the reduced-order models of both, nonparametrized LTI systems and parametrized LTI systems. The error bounds are the bounds for the difference between the transfer function of the original system and that of the reduced-order model, and are applicable to (P)MOR methods based on Petrov−Galerkin projection [16,18,19,21] and other methods that allow efficient residual evaluation of the output quantities.…”

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confidence: 99%

Somea posteriorierror bounds for reduced-order modelling of (non-)parametrized linear systems

2017

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Abstract. We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds.

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“…However, we do not expect a high accuracy in this variant unless the projection matrix V (p) is nearly constant with respect to the parameters. We refer to [13,34] for a good example of a projection matrix V (p) that strongly varies with respect to p. b) A more sophisticated approach uses samples p (1) , . .…”

Section: Parameterized Mor Approachmentioning

confidence: 99%

Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

Pulch

Maten

2015

Int. J. UncertaintyQuantification

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Linear dynamical systems are considered in the form of ordinary differential equations or differential algebraic equations. We change their physical parameters into random variables to represent uncertainties. A stochastic Galerkin method yields a larger linear dynamical system satisfied by an approximation of the random processes. If the original systems own a high dimensionality, then a model order reduction is required to

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Preserving the film coefficient as a parameter in the compact thermal model for fast electrothermal simulation

Cited by 51 publications

References 23 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

Somea posteriorierror bounds for reduced-order modelling of (non-)parametrized linear systems

Stochastic Galerkin Methods and Model Order Reduction for Linear Dynamical Systems

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