On the convergence of local expansions of layer potentials

Charles L. Epstein, Leslie Greengard, Andreas Kl̈Ockner

Research output: Contribution to journalArticlepeer-review

Abstract

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 or asymptotic analysis in potential theory.

Original languageEnglish (US)
Pages (from-to)2660-2679
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number5
DOIs
StatePublished - 2013

Keywords

  • Expansion
  • Helmholtz equation
  • Integral equations
  • Laplace equation
  • Layer potential
  • Quadrature
  • Singular integrals
  • Spherical harmonics

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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