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

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Author

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.

Department/s

Publishing year

2013

Language

English

Publication/Series

arXiv

Volume

http://arxiv.org/abs/1301.7276

Document type

Working paper

Publisher

Cornell University Library

Topic

  • Mathematics

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications