Effective Boundary Element Method for an Axisymmetrical Electromagnetic Field of a Layered Tube

Abstract

In this paper, an effective boundary element method with high accuracy for an axisymmetrical electromagnetlc field of a layered tube is developed. Quasi-static axisymmetrical Maxwell equations are represented by a vector potential satisfying Coulomb gauge and discretized with a standard BEM. The analytieal relationship between a magnetic field and a vector potential of an axisymmetrical eiectromagnetic field of a layered tube is derived using modified Bessel functions I₁ (z) and K₁ (z) and represented by products of transfer matrices. The discrete Fourier transform theory is applied to the analytical relationship, and the result is combined with the standard BEM. The distinct advantage of this method is that the discretization is not necessary in a layered tube. It is found that the length of the element which combines the standard BEM with the analytical relationship has upper and lower bounds in this method, because the discrete Fourier transform theory is based on the Shannon sampling theoren and a low-pass filter relates a magnetic field and a vector potential on the inner surface of a layered tube. The accuracy of this method is demonstrated by solving some example problems.