GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
Stress calculations on multiply connected domains
Journal of Computational Physics
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Journal of Computational Physics
Efficient discretization of Laplace boundary integral equations on polygonal domains
Journal of Computational Physics
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
Hi-index | 0.01 |
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.