Reduced-Order Models of Finite Element Approximations of Electromagnetic Devices Exhibiting Statistical Variability

Sumant, Prasad S.; Wu, Hangbin; Cangellaris, A.C.; Aluru, N. R.

doi:10.1109/tap.2011.2167935

Cited by 54 publications

(54 citation statements)

References 17 publications

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“…Therefore, the generalized polynomial chaos formalism [6], [7] was introduced as a more effective approach to rapidly model uncertainty due to variations in the input parameters. Recently, in addition to techniques that quickly determine statistical moments [8], [9], many new intrusive and nonintrusive procedures were proposed [10] and applied to transmission lines [11]- [15], multiport microwave circuits [16], [17], scattering [18]- [20] and antennas [15]. Yet, none of them is dedicated to wearable antenna design.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Technique Based on Polynomial Chaos to Model the Uncertainty in the Resonance Frequency of Textile Antennas Due to Bending

Boeykens

Rogier

Vallozzi

2014

IEEE Trans. Antennas Propagat.

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Abstract-The generalized polynomial chaos theory is combined with a dedicated cavity model for curved textile antennas to statistically quantify variations in the antenna's resonance frequency under randomly varying bending conditions. The nonintrusive stochastic method solves the dispersion relation for the resonance frequencies of a set of radius of curvature realizations corresponding to the Gauss quadrature points belonging to the orthogonal polynomials having the probability density function of the random variable as a weighting function. The formalism is applied to different distributions for the radius of curvature, either using a priori known or on the fly constructed sets of orthogonal polynomials. Numerical and experimental validation shows that the new approach is at least as accurate as Monte Carlo simulations while being at least 100 times faster. This makes the method especially suited as design tool to account for performance variability when textile antennas are deployed on persons with varying body morphology.

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Section: Introductionmentioning

confidence: 99%

An Efficient Technique Based on Polynomial Chaos to Model the Uncertainty in the Resonance Frequency of Textile Antennas Due to Bending

Boeykens

Rogier

Vallozzi

2014

IEEE Trans. Antennas Propagat.

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“…the application of the PC expansion to systems described by a large numbers of equations, such as the ones resulting by the use of EM methods, is not trivial due to the need of calculating an augmented system. Different techniques [9]- [13] have proposed PC-based methodologies for the VA of systems described by a large numbers of equations based on combinations of a PC expansion on the original system matrices and MOR techniques. Indeed, the MOR techniques allow to reduce the complexity of large scale models and, therefore, the computational cost of the simulations [14]- [16].…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, the MOR techniques allow to reduce the complexity of large scale models and, therefore, the computational cost of the simulations [14]- [16]. Recently, the techniques [11]- [13] propose a more general PC-based method for the VA of large scale systems described by Helmholtz equations. The recently proposed methods described in [11]- [13] are based on the following steps:…”

Section: Introductionmentioning

confidence: 99%

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Efficient Variability Analysis of Electromagnetic Systems Via Polynomial Chaos and Model Order Reduction

Spina

Ferranti

Antonini

et al. 2014

IEEE Trans. Compon., Packag. Manufact. Technol.

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Abstract-We present a novel technique to perform the model order reduction of multiport systems under the effect of statistical variability of geometrical or electrical parameters. The proposed approach combines a deterministic model order reduction phase with the use of the Polynomial Chaos expansion to perform the variability analysis of the system under study very efficiently. The combination of model order reduction and Polynomial Chaos techniques generates a final reduced-order model able to accurately perform stochastic computations and variability analysis. The novel proposed method guarantees a high-degree of flexibility, since different model order reduction schemes can be used and different types of modern electrical systems (e.g. filters, connectors) can be modeled. The accuracy and efficiency of the proposed approach is verified by means of two numerical examples and compared with other existing variability analysis techniques.

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“…Multi-resolution schemes [81,82] allows one to represent the random variables in terms of polynomial multi-wavelets. In [83][84][85], the PC expansion has been combined with model order reduction techniques to study systems described by a large set of equations. In [86], stochastic spectral methods have been applied to a hierarchical UQ of integrated circuits, while a gradient enhanced PC for circuit simulation has been introduced in [87].…”

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confidence: 99%

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

2018

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Advances in manufacturing process technology are key ensembles for the production of integrated circuits in the sub-micrometer region. It is of paramount importance to assess the effects of tolerances in the manufacturing process on the performance of modern integrated circuits. The polynomial chaos expansion has emerged as a suitable alternative to standard Monte Carlo-based methods that are accurate, but computationally cumbersome. This paper provides an overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems.

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Reduced-Order Models of Finite Element Approximations of Electromagnetic Devices Exhibiting Statistical Variability

Cited by 54 publications

References 17 publications

An Efficient Technique Based on Polynomial Chaos to Model the Uncertainty in the Resonance Frequency of Textile Antennas Due to Bending

An Efficient Technique Based on Polynomial Chaos to Model the Uncertainty in the Resonance Frequency of Textile Antennas Due to Bending

Efficient Variability Analysis of Electromagnetic Systems Via Polynomial Chaos and Model Order Reduction

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

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