Elimination of Computing Singular Surface Integrals in the PIES Method Through Regularization for Three-Dimensional Potential Problems

We propose a technique to circumvent the direct computation of singular surface integrals in parametric integral equation system (PIES) employed for solving three-dimensional potential problems. It is based on the regularization of the original singular PIES formula, resulting in the simultaneous elimination of both strongly and weakly singular integrals. As a result, there is the possibility of numerically calculating the values of all integrals in the obtained formula using standard Gaussian quadrature. The evaluation of accuracy for the proposed approach is examined through an illustrative case, specifically focusing on the steady-state temperature field distribution problem.