On the convergence of local expansions of layer potentials

2012/12/17 by Charles L. Epstein, Leslie Greengard, Epstein, Charles L. +3 · 2 citations
Engineering · Physics and Astronomy · #31A10 #65D32 #65N38 #65N80 #65R20 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1212.3868

openalex publication_date 2012/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Elementary Theory of Angular Momentum

Cited by

• Fast Evaluation of Derivatives of Green's Functions Using Recurrences
• Evaluation of layer potentials close to the boundary for Laplace and\n Helmholtz problems on analytic planar domains

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