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

Abstract

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.

Citation

Tytko, G. and Dawidowski, Ł. (2019), "Locating complex eigenvalues for analytical eddy-current models used to detect flaws", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 6, pp. 1800-1809. https://doi.org/10.1108/COMPEL-03-2019-0130