A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves
Författare
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.
Avdelning/ar
- Matematik LTH
- Harmonic Analysis and Applications
- eSSENCE: The e-Science Collaboration
Publiceringsår
2011
Språk
Engelska
Sidor
153-174
Publikation/Tidskrift/Serie
SIAM Journal on Scientific Computing
Volym
33
Issue
1
Fulltext
- Available as PDF - 308 kB
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Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Society for Industrial and Applied Mathematics
Ämne
- Mathematics
Nyckelord
- singular integral equation
- elasticity
- corner singularity
- multi-wedge points
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 1064-8275