Corpus ID: 15703187

High-order accurate Nystrom discretization of integral equations with weakly singular kernels on smooth curves in the plane

@article{Hao2011HighorderAN,
  title={High-order accurate Nystrom discretization of integral equations with weakly singular kernels on smooth curves in the plane},
  author={S. Hao and A. Barnett and P. Martinsson and P. Young},
  journal={arXiv: Numerical Analysis},
  year={2011}
}
Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarithmically-singular kernels. Only smooth boundaries are considered, but some of the techniques extend… Expand
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