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

2013/01/30 by Johan Helsing, Helsing, Johan · 2 citations
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1301.7276

openalex publication_date 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• High order regularization of nearly singular surface integrals
• Localized evaluation and fast summation in the extrapolated regularization method for integrals in Stokes flow

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