A sub-triangulation method to improve the accuracy of singular integral evaluation in 3-D boundary element methods

Methods of evaluating singular integrals arising when the boundary element method of minimum order is applied to 3-D eddy current problems are discussed. The nature of the singularities is briefly reviewed. Uniform and graded subtriangulation integration methods are described. A triangular-polar transformation is briefly outlined. The convergence of the uniform and graded subtriangulation schemes is examined for the case of 1/R and 1/R² singularities integrated over triangular elements. Also examined is the case in which the point of integration is near the triangular element. In the latter case, the graded subtriangulation method, coupled with Gauss integration, is shown to have computational advantages for weakly singular integrals when the point of observation is within the triangular surface element