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

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)153-174
TidskriftSIAM Journal on Scientific Computing
Volym33
Nummer1
DOI
StatusPublished - 2011

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Ämnesklassifikation (UKÄ)

  • Matematik

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