Exponential convergence for multipole and local expansions and their translations for sources in layered media: three-dimensional Laplace equation
Bo Wang,
Wenzhong Zhang,
Wei Cai
Abstract:In this paper, we prove the exponential convergence of the multipole and local expansions, shifting and translation operators used in fast multipole methods (FMMs) for 3-dimensional Laplace equations in layered media. These theoretical results ensure the exponential convergence of the FMM which has been shown by the numerical results recently reported in [9]. As the free space components are calculated by the classic FMM, this paper will focus on the analysis for the reaction components of the Green's function… Show more
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