Parameter preserving model order reduction for MEMS applications

Baur, Ulrike; Benner, Peter; Greiner, Andreas; Korvink, Jan G.; Lienemann, Jan; Moosmann, Christian

doi:10.1080/13873954.2011.547658

Cited by 48 publications

(41 citation statements)

References 16 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%

“…A computationally more efficient and reliable form is obtained if one uses the barycentric form of Lagrange interpolation [52]. Other choices are rational interpolation (which is used in [31] in barycentric form based on [51]), variants of Hermite interpolation, sinc or spline interpolation, etc. ; see [31] for experiments with some of these variants.…”

Section: Interpolating the Local Transfermentioning

confidence: 99%

“…Other choices are rational interpolation (which is used in [31] in barycentric form based on [51]), variants of Hermite interpolation, sinc or spline interpolation, etc. ; see [31] for experiments with some of these variants. These interpolation techniques can all be generalized to d > 1 using tensorization, but with limited success for growing dimension d of the parameter space.…”

Section: Interpolating the Local Transfermentioning

confidence: 99%

“…Since the expressions for the error bound depend strongly on the chosen interpolation method, we only provide a version for (polynomial) Lagrange interpolation, but writing the bounds down for other interpolation techniques is straightforward. For details, we refer the reader to the original sources [28,31]. Assume H is uniformly stable in Ω, at least K times differentiable with respect to p, and let Λ K−1 denote the Lebesgue constant of our node set {p 1 , .…”

Section: Interpolating the Local Transfermentioning

confidence: 99%

“…This strategy was studied in detail in [28,31]. Generally speaking, any interpolation technique could be used to select the functions L k (which also applies to (4.8)).…”

Section: Interpolating the Local Transfermentioning

confidence: 99%

See 4 more Smart Citations

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: Interpolating the Local Transfermentioning

confidence: 99%

Section: Interpolating the Local Transfermentioning

confidence: 99%

Section: Interpolating the Local Transfermentioning

confidence: 99%

“…This strategy was studied in detail in [28,31]. Generally speaking, any interpolation technique could be used to select the functions L k (which also applies to (4.8)).…”

Section: Interpolating the Local Transfermentioning

confidence: 99%

See 3 more Smart Citations

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

2015

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Linear and Nonlinear Model Order Reduction for MEMS Electrostatic Actuators

Lienemann

Bertarelli

Greiner

et al. 2013

Advanced Micro and Nanosystems

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Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

Yuan

Jiang

2022

Asian Journal of Control

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In this paper, a parametric model order reduction approach based on scaled Laguerre expansion series is investigated in frequency domain for large‐scale parametric systems. The proposed approach is implemented by two algorithms: the one‐sided algorithm and the two‐sided algorithm. Based on modified multi‐Arnoldi process for construction of projection matrices, reduced parametric systems with high fidelity are achieved in the full range of parametric domain. The reduced parametric systems obtained by the proposed algorithms preserve not only the parametric dependence of the original parametric system but also the first several Laguerre coefficients. The proposed algorithms are verified by two benchmarks (a synthetic parametric system and a microthruster unit). Comparisons of the results of original and reduced systems show that the obtained reduced systems have high fidelity.

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Parameter preserving model order reduction for MEMS applications

Cited by 48 publications

References 16 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

Linear and Nonlinear Model Order Reduction for MEMS Electrostatic Actuators

Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

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