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

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Author

Summary, in 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.

Department/s

Publishing year

2011

Language

English

Pages

153-174

Publication/Series

SIAM Journal on Scientific Computing

Volume

33

Issue

1

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Mathematics

Keywords

  • singular integral equation
  • elasticity
  • corner singularity
  • multi-wedge points

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 1064-8275