High precision numerical integration methods for 3-D boundary element analysis [of electromagnetic problems]

In the analysis of three-dimensional electromagnetic problems using the boundary-element method, the accurate calculation of nearly singular integrals determines the credibility of the analysis. To this end, the author earlier proposed the PART method (1988). In the present work, he proposes using polar coordinates in the plane tangent to the element at the point nearest to the source point, and then transforming the radial variable by the single or double exponential transformation, after which the truncated trapezium rule is applied. Numerical results show that exponential-type transformations give accurate results for nearly singular integrals and have the advantage of not requiring any integration tables. However, they are not as efficient as the PART method regarding CPU-time. Hence, when a reliable Gauss-Legendre formula table for many integration points is available, the PART method should be used. When such a table is not available, the proposed method with the single exponential radial variable transformation should be used, especially for flux calculations at points very near the boundary