APPLICATION OF THE BOUNDARY ELEMENT METHOD AND THE IMPEDANCE BOUNDARY CONDITION IN T-W AND 2-D EDDY CURRENT PROBLEMS

New formulations are presented for the induction problem where the evaluation of the electromagnetic fields induced in and the power flow to a magnetic or nonmagnetic conducting cylinder placed in the vicinity of a known source place in free space is considered. The mathematical model is derived for an infinitely long cylinder with arbitrary cross sections. The materials of the cylinders are assumed to have arbitrary constant scalar properties. The source is time harmonic with arbitrary frequency. The boundary value problem of the travelling wave case is recasted in surface-type integral equation form. Two different procedures are presented. The highest singularity occurring in the first formulation is of order 0(R('-1)) which is a strong singularity, however, it is lower than that presented in previous literature. The second formulation is easier to derive, yet the highest singularity is a logarithmic singularity which requires no special numerical treatment. The special cases of transverse-magnetic (TM) and transverse-electric (TE) two-dimensional problems are deduced easily from the travelling wave formulations. For the two dimensional problem as well as for the travelling-wave one the following special cases are presented: (1) The quasi-magnetostatic case. (2) Magnetostatic case. (3) Perfectly conducting cylinder. A novel approach in which the impedance boundary condition (IBC) is used to reduce the number of unknowns to one half of the original number. A detailed investigation of the IBC approximation is presented. Two different IBC approaches are considered. The first, called a combined IBC method, formulates the problem in terms of the internal and external fundamental solutions. The second, called an external IBC formulation, utilizes only the external fundamental solution. The combined and the external IBC formulations are given for three-dimensional, travelling wave and two-dimensional problems.;The application of the boundary element method (BEM) for the numerical solution of the boundary integral equations (BIE's) is demonstrated. Results are obtained for two-dimensional problems using the exact formulation and the IBC formulations.;For the travelling wave problem, results are first obtained using the exact formulation integral equations in which all the kernels are regular or at the most weakly singular. The numerical treatments of strongly singular kernels are explained in detail.;A detailed analysis of the edge effects is presented numerically. The conditions under which infinite fields can exist at edges are examined and compared with the previous theoretical literature. (Abstract shortened with permission of author.)...