Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Journal of Computational Physics
A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Nyström method for weakly singular integral operators on surfaces
Journal of Computational Physics
Hi-index | 31.45 |
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.