Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples

Strakova, Erika; Lukáš, Dalibor; Vodstrčil, Petr

doi:10.15598/aeee.v15i2.2252

Cited by 3 publications

(3 citation statements)

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“…Using (20), the poles (in s domain) are in agreement with (21). It can be seen that all five poles are now near to each other and to jω axis.…”

Section: Applications For Microwave Filters a Applications I: Classical Filterssupporting

confidence: 54%

“…It should be emphasized here that without the use of Belevitch determinant in (15), the argument principle could not be applied directly if f (s) contains both poles and zeros in the LHP. Most argument principle based methods such as [20], [21] are able to solve only for the zeros of f (s) when it is analytic within C (P = 0).…”

Section: Application Of Belevitch Theorem For Pole-zero Analysismentioning

confidence: 99%

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Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements

Tan

Heh

2018

IEEE Trans. Microwave Theory Techn.

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“…Using (20), the poles (in s domain) are in agreement with (21). It can be seen that all five poles are now near to each other and to jω axis.…”

Section: Applications For Microwave Filters a Applications I: Classical Filterssupporting

confidence: 54%

Section: Application Of Belevitch Theorem For Pole-zero Analysismentioning

confidence: 99%

Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements

Tan

Heh

2018

IEEE Trans. Microwave Theory Techn.

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“…The second way of finding discrete eigenvalues is based on the methods of computing complex roots by means of the Cauchy argument principle (Davies, 1986;Dellnitz et al, 2002;Strakova et al, 2017). In the approach proposed by Delves and Lyness (1967), what is examined first is the number of roots inside a contour that constitutes the solution domain.…”

Section: Introductionmentioning

confidence: 99%

Locating complex eigenvalues for analytical eddy-current models used to detect flaws

Tytko

Dawidowski

2019

COMPEL

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Purpose Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function. Design/methodology/approach The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them. Findings The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time. Originality/value The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.

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Pulse-Modulation Eddy Current Evaluation of Interlaminar Corrosion in Stratified Conductors: Semi-Analytical Modeling and Experiments

Liu

Ren

et al. 2022

Sensors

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Interlaminar corrosion (ILC) poses a severe threat to stratified conductors which are broadly employed in engineering fields including aerospace, energy, etc. Therefore, for the pressing concern regarding the safety and integrity of stratified conductors, it is imperative to non-intrusively and quantitatively interrogate ILC via non-destructive evaluation techniques. In this paper, pulse-modulation eddy current (PMEC) for imaging and assessment of ILC is intensively investigated through theoretical simulations and experiments. A semi-analytical model of PMEC evaluation of ILC occurring at the interlayer of two conductor layers is established based on the extended truncated region eigenfunction expansion (ETREE) along with the efficient algorithm for the numerical computation of eigenvalues for reflection coefficients of the stratified conductor under inspection. Based on theoretical investigation, PMEC evaluation of ILC in testing samples are further scrutinized by using the PMEC imaging system built up for the experimental study. The theoretical and experimental results have revealed the feasibility of PMEC for imaging and evaluation of ILC in stratified conductors.

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Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples

Cited by 3 publications

References 0 publications

Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements

Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements

Locating complex eigenvalues for analytical eddy-current models used to detect flaws

Pulse-Modulation Eddy Current Evaluation of Interlaminar Corrosion in Stratified Conductors: Semi-Analytical Modeling and Experiments

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