Using Krylov‐Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain

Ya, Yao; Meerbergen, Karl

doi:10.1002/nme.3357

Cited by 19 publications

(22 citation statements)

References 34 publications

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“…• (P)MOR based on projection using local bases These methods build the bases Q and U only using the data computed at a given parameter value, say p 0 . The resulting ROM is valid for p 0 , but if derivative information with respect to p is also included in Q and U , we can obtain a local pROM [8,19,20]. This type of (p)ROMs can be used as the building blocks in our proposed pole-matching PMOR method.…”

Section: Projection-based (P)mormentioning

confidence: 99%

Reduced-order modelling of parametric systems via interpolation of heterogeneous surrogates

Feng

Benner

2019

Adv. Model. and Simul. in Eng. Sci.

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This paper studies parametric reduced-order modeling via the interpolation of linear multiple-input multiple-output reduced-order, or, more general, surrogate models in the frequency domain. It shows that realization plays a central role and two methods based on different realizations are proposed. Interpolation of reduced-order models in the Loewner representation is equivalent to interpolating the corresponding frequency response functions. Interpolation of reduced-order models in the (real) pole-residue representation is equivalent to interpolating the positions and residues of the poles. The latter pole-matching approach proves to be more natural in approximating system dynamics. Numerical results demonstrate the high efficiency and wide applicability of the pole-matching method. It is shown to be efficient in interpolating surrogate models built by several different methods, including the balanced truncation method, the Krylov method, the Loewner framework, and a system identification method. It is even capable of interpolating a reduced-order model built by a projection-based method and a reduced-order model built by a data-driven method. Its other merits include low computational cost, small size of the parametric reduced-order model, relative insensitivity to the dimension of the parameter space, and capability of dealing with complicated parameter dependence.

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Section: Projection-based (P)mormentioning

confidence: 99%

Reduced-order modelling of parametric systems via interpolation of heterogeneous surrogates

Feng

Benner

2019

Adv. Model. and Simul. in Eng. Sci.

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“…In this application, we consider the model of a floor inside a building [13] with dimensions 10m × 10m × 0.3m. Its Young's modulus, Poisson's ratio, proportional damping ratio and density are respectively 30GPa, 0.3, 0.1 and 2500 kg/m 3 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output

Beeumen

Meerbergen

2010

AIP Conference Proceedings

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Balanced truncation is a widely used and appreciated projection-based model reduction technique for linear systems. This technique has the following two important properties: approximations by balanced truncation preserve the stability and the H ∞ -norm (the maximum of the frequency response) of the error system is bounded above by twice the sum of the neglected singular values. This paper tries to extend the framework of linear balanced truncation to systems with a quadratic output. For such systems, the controllability Gramian remains the same. The observability Gramian is computed from a linear system with multiple outputs that is derived from the quadratic output of the original system. We give a numerical example for a large-scale system arising from structural analysis.

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“…This is usually referred to as parametric model reduction (PMR). It has found immediate applications in inverse problems [87,49,69,41,37], optimization [11,7,94,95,8], and design and control [70,5,36,15,45,71,62]. There are various approaches to parametric model reduction methods; see, e.g., [78,79,33,75,13,60,62,85,34] and the references therein.…”

Section: Interpolatory Model Reduction Of Parametric Systemsmentioning

confidence: 99%

Chapter 7: Model Reduction by Rational Interpolation

Beattie¹,

Gugercin²

2017

Model Reduction and Approximation

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The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined methods for deriving interpolatory reduced models directly from input/output measurements; and extensions for the reduction of parametrized systems. This chapter offers a survey of interpolatory model reduction methods starting from basic principles and ranging up through recent developments that include weighted model reduction and structure-preserving methods based on generalized coprime representations. Our discussion is supported by an assortment of numerical examples.Mathematics Subject Classification (2010). 41A05, 93A15, 93C05, 37M99.

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Using Krylov‐Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain

Cited by 19 publications

References 34 publications

Reduced-order modelling of parametric systems via interpolation of heterogeneous surrogates

Reduced-order modelling of parametric systems via interpolation of heterogeneous surrogates

Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output

Chapter 7: Model Reduction by Rational Interpolation

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