Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

Abstract

Simple and efficient numerical procedures for evaluating the gradient of Helmholtz-type potentials are presented. The convergence behavior of both normal and tangential components of the gradient is examined. It is also shown that the scheme for handling near-hypersingular integrals is effective for handling nearly singular potential integrals as well, so the same quadrature scheme may be used for both simultaneously.