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

In English

Författare

Summary, in English

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.

Avdelning/ar

Publiceringsår

2013

Språk

Engelska

Publikation/Tidskrift/Serie

arXiv

Volym

http://arxiv.org/abs/1301.7276

Dokumenttyp

Working paper

Förlag

Cornell University Library

Ämne

  • Mathematics

Status

Published

Forskningsgrupp

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications