Iterative solution of linear systems arising from the boundary integral method
SIAM Journal on Scientific and Statistical Computing
Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Computational Physics
Efficient discretization of Laplace boundary integral equations on polygonal domains
Journal of Computational Physics
A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
SIAM Journal on Scientific Computing
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Advances in Computational Mathematics
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We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace's equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.