A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves
(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:
https://lup.lub.lu.se/record/1781825
- author
- Helsing, Johan LU
- organization
- publishing date
- 2011
- 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
- 2022-01-26 06:52:23
@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}},
keywords = {{singular integral equation; elasticity; corner singularity; multi-wedge points}},
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}},
}