On the numerical evaluation of the singular integrals of scattering theory

In a previous work, the authors introduced a scheme for the numerical evaluation of the singular integrals which arise in the discretization of certain weakly singular integral operators of acoustic and electromagnetic scattering. That scheme is designed to achieve high-order algebraic convergence and high-accuracy when applied to operators given on smoothly parameterized surfaces. This paper generalizes the approach to a wider class of integral operators including many defined via the Cauchy principal value. Operators of this type frequently occur in the course of solving scattering problems involving boundary conditions on tangential derivatives. The resulting scheme achieves high-order algebraic convergence and approximately 12 digits of accuracy.