Abstract
An effective boundary element method with high accuracy for an axisymmetrical electromagnetio field of a layered plate is developed. Quasi-static axisymmetrical Maxwell equations are represented by a vector potential which satisfies the coulomb gauge, and discretized using a standard BEM. Analytical relationships between the magnetic field and the vector potential of an axisymmetrical electromagnetic field are derived for two cases : (1) a layered plate, and (2) a plate whose near-surface conductivity varies as a hyperbolic tangent function of depth. For case (1), the relationship is represented by products of the transfer matrices. For case (2), the relationship is represented by a hypergeometric function. The discrete Hankel transform theory is applied to these analytical relationships, and the result is combined with the standard BEM. The distinct advantage of this method is that discretization is not necessary in a layered plate. It is found that the length of the element that combines the standard BEM with the analytical relationship has a lower limit in this method, because the analytical relationships can be considered as a low-pass filter which relates the magnetic field to the vector potential on the upper surface of a layered plate. The accuracy of this method is demonstrated by solving some example problems.
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