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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)
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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
SIAM Publications
external identifiers
  • wos:000287697800007
  • scopus:79952301334
ISSN
1064-8275
DOI
10.1137/090779218
language
English
LU publication?
yes
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
2011-07-14 11:18:03
date last changed
2017-11-12 03:17:40
@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},
  keyword      = {singular integral equation,elasticity,corner singularity,multi-wedge points},
  language     = {eng},
  number       = {1},
  pages        = {153--174},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Scientific Computing},
  title        = {A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves},
  url          = {http://dx.doi.org/10.1137/090779218},
  volume       = {33},
  year         = {2011},
}