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This note is about promoting singularity subtraction as a helpful tool in thediscretization of singular integral operators on curved surfaces. Singular andnearly singular kernels are expanded in series whose terms are integrated onparametrically rectangular regions using high-order product integration,thereby reducing the need for spatial adaptivity and precomputed weights. Asimple scheme is presented and an application to the interior Dirichlet Laplaceproblem on some tori gives around ten digit accurate results using only twoexpansion terms and a modest programming- and computational effort.

A higher-order singularity subtraction technique for the discretization of singular integral operators on curved surfaces