Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation

It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace׳s and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.