| Title | A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves |
| Authors | Johan Helsing |
| Alternative Location | http://www.maths.lth.se/na/... |
| Alternative Location | http://dx.doi.org/10.1137/0..., Restricted Access |
| Publication | SIAM Journal on Scientific Computing |
| Year | 2011 |
| Volume | 33 |
| Issue | 1 |
| Pages | 153 - 174 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Society for Industrial and Applied Mathematics |
| Abstract English | 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. |
| Keywords | singular integral equation, elasticity, corner singularity, multi-wedge points, |
| ISBN/ISSN/Other | ISSN: 1095-7197 |
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Last update: 2013-04-11
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