High accuracy integration of boundary integral equations describing axisymmetric field problems

The accuracy of solutions to boundary integral equations depends strongly on the quality of the numerical method by which the singularities of the kernel are integrated. Results of high precision are obtained by transforming the singular part of the kernel and applying Gaussian integration, where the combination of both methods can be considered as a new approach. In addition to the well-known tanh transformation, we present the arctan transformation as a new procedure, furthermore, we inspect the properties of the erf transformation. For rotation-symmetric problems, the numerical parameters of these three transformations are thoroughly investigated.