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

Helsing, Johan LU (2013) In arXiv http://arxiv.org/abs/1301.7276.
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
published
subject
in
arXiv
volume
http://arxiv.org/abs/1301.7276
pages
7 pages
publisher
Cornell University Library
language
English
LU publication?
yes
id
6f52485b-47f8-4be9-a562-c2f546655277 (old id 4113953)
alternative location
http://www.maths.lth.se/na/staff/helsing/tori.pdf
date added to LUP
2013-11-18 15:01:22
date last changed
2016-10-27 11:07:21
@misc{6f52485b-47f8-4be9-a562-c2f546655277,
  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.},
  author       = {Helsing, Johan},
  language     = {eng},
  pages        = {7},
  publisher    = {ARRAY(0xaf20340)},
  series       = {arXiv},
  title        = {A higher-order singularity subtraction technique for the discretization of singular integral operators on curved surfaces},
  volume       = {http://arxiv.org/abs/1301.7276},
  year         = {2013},
}