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A fast and stable solver for singular integral equations on piecewise smooth curves. (English) Zbl 1227.65132
Summary: 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.

65R20Integral equations (numerical methods)
45E05Integral equations with kernels of Cauchy type
74R10Brittle fracture
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