Segregation by primary phase factors

Klemas, Thomas J.; Daniel, Luca; White, Jacob K.

doi:10.1145/1065579.1065825

Cited by 6 publications

(1 citation statement)

References 18 publications

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“…MOR techniques have been proposed to address the computational complexity associated with the analysis of large systems of delayed equations [79,[83][84][85][86][87][88]. In order to provide the foundation for the motivation and understanding of our proposed PMOR method, a brief description of MOR as applied to τ -PEEC circuits is described in the next section.…”

Section: Peec Equationsmentioning

confidence: 99%

Uncertainty Quantification in Large Scale Systems Design

Ye¹

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One of the main challenges facing designers of high-speed integrated circuits and interconnects is predicting the effect of the variability of geometrical and physical parameters on the circuit performance. Monte Carlo (MC) simulation has been traditionally used in commercial circuit and electromagnetic (EM) simulators for predicting the statistical distribution of circuit and system performance metrics. However, the high computational cost associated with the MC simulation is a significant limiting factor especially for large circuits.In this thesis, an algorithm based on Parametric Model Order Reduction (PMOR) is presented for statistical analysis of large microwave and high-speed circuits with multiple stochastic parameters. Using the proposed algorithm, a set of local reducedorder parameterized circuits are derived based on adaptive frequency sampling and implicit multi-moment matching projection techniques. The local models preserve the stochastic parameters as symbolic quantities. As a result, stochastic response of the circuit can be obtained by simulating the local reduced models instead of the original large system leading to significant reduction in the computational cost compared to traditional Monte-Carlo techniques.In addition, a method is presented for high-dimensional variability analysis. This algorithm is based on two main concepts, namely node tearing for parameter partitioning and sparse grid interpolation. Node-tearing is used to localize the parameters I would also like to thank the staff at department of Electronics in Carleton University, especially Mrs. Blazenka Power. Their constantly and patiently supports made this adventure so much easier and for that, I am thankful.In the end, I would like to express my deep love to my parents for their love and care. Without their encouragement, I could not have reached this far. What they have sacrificed, I could not forget. Their courage, always inspires me. To them, I dedicate this thesis. vi

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Section: Peec Equationsmentioning

confidence: 99%

Uncertainty Quantification in Large Scale Systems Design

Ye¹

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A hybrid adaptive sampling algorithm for obtaining reduced order models for systems with frequency dependent state‐space matrices

Samuel

Ferranti

Knockaert

et al. 2015

Int J Numerical Modelling

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This paper proposes a hybrid adaptive sampling algorithm to automate the generation of reduced order models for systems described by large-scale frequency dependent state-space models. The evaluation of the frequency dependent state-space model for each frequency sample can be computationally expensive. The distribution of frequency samples must be optimized to avoid oversampling and undersampling. In order to have an optimum number of frequency samples, the proposed algorithm uses the reflective exploration technique for the adaptive selection of samples, and the sampling is further refined using a binary search to validate the frequency dependent reduced order models. Projection-based model order reduction techniques are used for obtaining the reduced order model. The projection matrix for each frequency sample is merged to obtain a common projection matrix for all samples. However, in certain cases when the number of sample points increases, the merged projection matrix also increases in dimension and might fail to provide a satisfactory reduction in model size. Thus, the merged projection matrix is truncated based on its singular values to obtain a compact common projection matrix. Then, the reduced order state-space matrices per frequency are interpolated over the frequency range of interest to obtain the system response. Pertinent examples validate the proposed hybrid adaptive sampling algorithm. Copyright (C) 2015 John Wiley & Sons, Ltd

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