A higher-order singularity subtraction technique for the discretization of singular integral operators on curved surfaces
This work offers a practical, high-order method for solving singular integral equations on curved surfaces, reducing the need for spatial adaptivity and precomputed weights, which is beneficial for computational scientists working on boundary integral equations.
The paper presents a singularity subtraction technique for discretizing singular integral operators on curved surfaces, achieving around ten-digit accuracy on the interior Dirichlet Laplace problem on tori using only two expansion terms with modest computational effort.
This note is about promoting singularity subtraction as a helpful tool in the discretization of singular integral operators on curved surfaces. Singular and nearly singular kernels are expanded in series whose terms are integrated on parametrically rectangular regions using high-order product integration, thereby reducing the need for spatial adaptivity and precomputed weights. A simple scheme is presented and an application to the interior Dirichlet Laplace problem on some tori gives around ten digit accurate results using only two expansion terms and a modest programming- and computational effort.