Second kind integral equation formulation of Stokes' flows past a particle of arbitary shape
SIAM Journal on Applied Mathematics
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
A New Spectral Boundary Integral Collocation Method for Three-Dimensional Potential Problems
SIAM Journal on Numerical Analysis
Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystro¨m discretization
Journal of Computational Physics
Wavelet Galerkin Algorithms for Boundary Integral Equations
SIAM Journal on Scientific Computing
Quadrature methods for 2D and 3D problems
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Journal of Computational Physics
Multiscale Bases for the Sparse Representation of Boundary Integral Operators on Complex Geometry
SIAM Journal on Scientific Computing
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
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Convergence and conditioning results are presented for the lowest-order member of a family of Nyström methods for arbitrary, exterior, three-dimensional Stokes flow. The flow problem is formulated in terms of a recently introduced two-parameter, weakly singular boundary integral equation of the second kind. In contrast to methods based on product integration, coordinate transformation and singularity subtraction, the family of Nyström methods considered here is based on a local polynomial correction determined by an auxiliary system of moment equations. The polynomial correction is designed to remove the weak singularity in the integral equation and provide control over the approximation error. Here we focus attention on the lowest-order method of the family, whose implementation is especially simple. We outline a convergence theorem for this method and illustrate it with various numerical examples. Our examples show that well-conditioned, accurate approximations can be obtained with reasonable meshes for a range of different geometries.