Sensitivity analysis and optimization of eigenmode localization in continuum systems

Zhang, Zhengfang; Chen, Weifeng; Cheng, Xiaoliang

doi:10.1007/s00158-015-1235-y

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…Here, b ≡ 0 and we have either a ≡ 1 and c = n 2 (TM mode problem) or a = 1/n 2 and c ≡ 1 (TE mode problem), where n = n(x, y) is the refractive index of the PCF. The refractive index can be subject to uncertainty, due to heterogeneities or impurities in the material and due to geometric variations [15,41].…”

Section: Introductionmentioning

confidence: 99%

Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

et al. 2019

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We consider the forward problem of uncertainty quantification for the generalised Dirichlet eigenvalue problem for a coercive second order partial differential operator with random coefficients, motivated by problems in structural mechanics, photonic crystals and neutron diffusion. The PDE coefficients are assumed to be uniformly bounded random fields, represented as infinite series parametrised by uniformly distributed i.i.d. random variables. The expectation of the fundamental eigenvalue of this problem is computed by (a) truncating the infinite series which define the coefficients; (b) approximating the resulting truncated problem using lowest order conforming finite elements and a sparse matrix eigenvalue solver; and (c) approximating the resulting finite (but high dimensional) integral by a randomly shifted quasi-Monte Carlo lattice rule, with specially chosen generating vector. We prove error estimates for the combined error, which depend on the truncation dimension s, the finite element mesh diameter h, and the number of quasi-Monte Carlo samples N . Under suitable regularity assumptions, our bounds are of the particular form O(h 2 + N −1+δ ), where δ > 0 is arbitrary and the hidden constant is independent of the truncation dimension, which needs to grow as h → 0 and N → ∞. As for the analogous PDE source problem, the conditions under which our error bounds hold depend on a parameter p ∈ (0, 1) representing the summability of the terms in the series expansions of the coefficients. Although the eigenvalue problem is nonlinear, which means it is generally considered harder than the source problem, in almost all cases (p = 1) we obtain error bounds that converge at the same rate as the corresponding rate for the source problem. The proof involves a detailed study of the regularity of the fundamental eigenvalue as a function of the random parameters. As a key intermediate result in the analysis, we prove that the spectral gap (between the fundamental and the second eigenvalues) is uniformly positive over all realisations of the random problem.

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Section: Introductionmentioning

confidence: 99%

Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

et al. 2019

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“…The peaks at 710.0 eV and 723.4 eV from the Fe2p spectrum are attributed to iron oxide and ferrous disulfide. These results indicate that the OA‐AMPS copolymer in water reacts with the surface of the metal during the friction process …”

Section: Resultsmentioning

confidence: 76%

Synthesis of a water‐soluble, rubber seed oil–based sulfonate and its tribological properties as a water‐based lubricant additive

Ding

Wang

et al. 2017

J of Applied Polymer Sci

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A novel, water-based oleic acid (OA)/2-acryloylamino-2-methyl-1-propanesulfonic acid (AMPS) copolymer was successfully synthesized as a water-based lubricant additive. The OA-AMPS copolymer was characterized by Fourier transform infrared and proton NMR spectroscopies and then used as a lubricant additive in water. The lubrication properties of water-miscible cutting fluids with the OA-AMPS copolymer additive were investigated using a four-ball friction tester. The surface of the wear scars was explored using scanning electron microscopy and X-ray photoelectron spectroscopy. The addition of the synthesized OA-AMPS copolymer improved the friction coefficient and wear scar diameter of water. The maximum nonseizure load increased from 95 to 431 N, and the anticorrosion ability on copper was categorized as 1b. Good antiwear and friction-reducing properties for water were observed and attributed to the absorption and tribochemical films composed of iron oxide and ferrous disulfide.

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“…A numerical method of solution was developed by the authors to determine an ascent direction in the design space for the smallest eigenvalue. More recently, a simple strategy proposed by Zhang et al [2015] can be used in order to deal with multiplicity of eigenmodes, which consists in select the closest eigenmode to the current one. See also the paper by Torii and Rocha de Faria [2017] for more sophisticated approach based on a smooth p-norm approximation for the smallest eigenvalue.…”

Section: Eigenvalue Of the Laplace Problemmentioning

confidence: 99%

Model-based and Signal-Based Inverse Methods

2022

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The engineering sector drives and enables the development of a country. The formation of an engineer allows a technical capacity to evaluate, plan, design, suggest and apply all possible techniques in search of the best construction of a technological equipment. Currently, the engineer must be more and more prepared to solve existing problems in various sectors of society. It is through it that societies grow in search of progress. The recognition of engineering and the training of new professionals increases every year in Brazil. In the 2000s, the University of Brasília (UnB) went through an expansion process, resulting in the implementation of the new UnB Engineering Campus in the city of Gama (UnB-Gama, FGA). Five new undergraduate courses were created: Aerospace Engineering, Automotive Engineering, Electronic Engineering, Energy Engineering and Software Engineering. The UnB Gama Campus project converges to increase the education level of the Brazilian population, especially in the five areas of engineering activity, all in line with current national public policies, aimed at expanding the population's access to quality higher education in the country. Following the high quality teaching line, the UnB-Gama campus has the Graduate Program in Integrity of Engineering Materials (PPG-Integridade). The program has the following lines of research: Dynamics and Vibrations, Fatigue, Structural Materials, Biomaterials, Structure Fluid Interaction and Numerical Simulation of the Mechanical Behavior of Materials. This book series is an initiative of PPG-Integridade -UnB, organized as a collaborative work involving researchers, engineers, scholars, from several institutions, universities, industry, recognized both nationally and internationally.Beside the high technical quality and relevance of the topics covered in the books, this series will enable an essential internationalization of the research currently developed within the University of Brasília. Several authors from different countries also contributed to these books, enabling greater interaction between national and international research groups. This internationalization raises the level of academic education for new professionals in the field of engineering, in addition to more advanced scientific research and technological development. Additionally, this book series features a strong contribution from the industrial sector. Several professionals from different companies collaborated with the writing of some chapters in the three volumes that make up this series. These initiatives are of great strategic importance, as they allow the grouping of different technical capabilities. On the part of companies in the sector, with knowledge of market demands, and on the part of universities, by adding the technical-scientific knowledge of their team of researchers to the improvement of innovative products and services. This book should be appreciated by anyone in need of knowledge of Materials Integrity. The completeness of Discrete Modeling and Inverse Methods theory c...

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Sensitivity analysis and optimization of eigenmode localization in continuum systems

Cited by 6 publications

References 32 publications

Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

Synthesis of a water‐soluble, rubber seed oil–based sulfonate and its tribological properties as a water‐based lubricant additive

Model-based and Signal-Based Inverse Methods

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