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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
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-dimensiona…
Fast multipole method for 3-D Laplace equation in layered media
Bo Wang, Wen Zhong Zhang, Wei Cai
In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free…
A Path Integral Monte Carlo Method based on Feynman-Kac Formula for Electrical Impedance Tomography
Yijing Zhou, Wei Cai
A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical im…
Fast Multipole Method For 3-D Helmholtz Equation In Layered Media
Bo Wang, Wenzhong Zhang, Wei Cai
In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for th…