An Efficient Semianalytical Method for Hypersingularity Treatment Over Curved Patches

In this communication, we propose an efficient method to evaluate hypersingular integrals defined on curved surfaces. First an exact expression for hypersingular kernel is derived by projecting the integral on curvilinear element on a flat surface. Next singularity subtraction employed, where the singular core is hypersingular and the remaining part is weakly singular. The singular core is evaluated analytically using finite part interpretation and the remaining weakly singular part is evaluated numerically using Gauss-Legendre quadrature rules. By numerical experiments we have shown that the convergence rate of the purposed method is quite high even for few number of quadrature nodes. Accuracies over ten digits are obtained for relatively large and highly curved surfaces, which may cover entire domain of local corrections in Nyström method.