On the Convergence of Local Expansions of Layer Potentials

@article{Epstein2013OnTC,
  title={On the Convergence of Local Expansions of Layer Potentials},
  author={Charles L. Epstein and Leslie Greengard and Andreas Kl{\"o}ckner},
  journal={SIAM J. Numerical Analysis},
  year={2013},
  volume={51},
  pages={2660-2679}
}
In a recently developed quadrature method (quadrature by expansion or QBX), it was demonstrated that weakly singular or singular layer potentials can be evaluated rapidly and accurately on-surface by making use of local expansions about carefully chosen off-surface points. In this paper, we derive estimates for the rate of convergence of these local expansions, providing the analytic foundation for the QBX method. The estimates may also be of mathematical interest, particularly for microlocal… CONTINUE READING
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