Computation of the Eigenvalues for Bounded Domain Eddy-Current Models With Coupled Regions

A bounded domain of eddy-current problems leads to discrete eigenvalues and it allows one to satisfy the interface conditions between coupled regions simultaneously along two coordinates. The eigenvalues are zeros of complex domain functions that, for many eddy-current applications, have the same tr...

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Vydáno v:IEEE transactions on magnetics Ročník 52; číslo 6; s. 1 - 10
Hlavní autoři: Vasic, Darko, Ambrus, Davorin, Bilas, Vedran
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.06.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Argument principle
Computation
Computational modeling
Eddy current testing
Eddy currents
eigenvalue equations
Eigenvalues
Eigenvalues and eigenfunctions
electromagnetic modelling
Joining
Magnetic domains
Magnetism
Mathematical analysis
Mathematical model
Mathematical models
Numerical models
Poles and zeros
Trigonometric functions
eddy currents
electromagnetic modeling
Argument principle
eigenvalue equations
eigenvalues and eigenfunctions
ISSN:0018-9464, 1941-0069
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Popis
Shrnutí:A bounded domain of eddy-current problems leads to discrete eigenvalues and it allows one to satisfy the interface conditions between coupled regions simultaneously along two coordinates. The eigenvalues are zeros of complex domain functions that, for many eddy-current applications, have the same trigonometric form due to the sine and cosine terms in a corresponding general solution of the governing Helmholtz equation. We examine the functions' properties: 1) pole locations and multiplicity; 2) zero levelsets; and 3) region enclosing the zeros. These properties allow the construction of reliable and efficient algorithms for the eigenvalue computation, which are essential for bounded domain eddy-current models with coupled regions. We propose such an algorithm based on Cauchy's argument principle. We verify the algorithm using dimensions and materials typically encountered in diverse practical applications. The proposed algorithm performance is compared with the performance of an algorithm based on the Netwton-Raphson method.
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ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2016.2518993