Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves

Helsing, Johan LU (2011) In SIAM Journal on Scientific Computing 33(1). p.153-174
Abstract
A scheme for the numerical solution of singular integral equations on piecewise smooth curves is presented. It relies on several techniques: reduction, Nyström discretization, composite quadrature, recursive compressed inverse preconditioning, and multipole acceleration. The scheme is fast and stable. Its computational cost grows roughly logarithmically with the precision sought and linearly with overall system size. When the integral equation models a boundary value problem, the achievable accuracy may be close to the condition number of that problem times machine epsilon. This is illustrated by application to elastostatic problems involving zigzag-shaped cracks with up to twenty thousand corners and branched cracks with hundreds of... (More)
A scheme for the numerical solution of singular integral equations on piecewise smooth curves is presented. It relies on several techniques: reduction, Nyström discretization, composite quadrature, recursive compressed inverse preconditioning, and multipole acceleration. The scheme is fast and stable. Its computational cost grows roughly logarithmically with the precision sought and linearly with overall system size. When the integral equation models a boundary value problem, the achievable accuracy may be close to the condition number of that problem times machine epsilon. This is illustrated by application to elastostatic problems involving zigzag-shaped cracks with up to twenty thousand corners and branched cracks with hundreds of triple junctions. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
singular integral equation, elasticity, corner singularity, multi-wedge points
in
SIAM Journal on Scientific Computing
volume
33
issue
1
pages
153 - 174
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • wos:000287697800007
  • scopus:79952301334
ISSN
1064-8275
DOI
10.1137/090779218
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
812c98d4-8b2b-43bb-bd96-9669692fe3eb (old id 1781825)
alternative location
http://www.maths.lth.se/na/staff/helsing/SISC11.pdf
date added to LUP
2016-04-01 11:17:02
date last changed
2021-09-22 01:24:05
@article{812c98d4-8b2b-43bb-bd96-9669692fe3eb,
  abstract     = {A scheme for the numerical solution of singular integral equations on piecewise smooth curves is presented. It relies on several techniques: reduction, Nyström discretization, composite quadrature, recursive compressed inverse preconditioning, and multipole acceleration. The scheme is fast and stable. Its computational cost grows roughly logarithmically with the precision sought and linearly with overall system size. When the integral equation models a boundary value problem, the achievable accuracy may be close to the condition number of that problem times machine epsilon. This is illustrated by application to elastostatic problems involving zigzag-shaped cracks with up to twenty thousand corners and branched cracks with hundreds of triple junctions.},
  author       = {Helsing, Johan},
  issn         = {1064-8275},
  language     = {eng},
  number       = {1},
  pages        = {153--174},
  publisher    = {Society for Industrial and Applied Mathematics},
  series       = {SIAM Journal on Scientific Computing},
  title        = {A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves},
  url          = {https://lup.lub.lu.se/search/files/2530288/3878571.pdf},
  doi          = {10.1137/090779218},
  volume       = {33},
  year         = {2011},
}