Extending the fast multipole method to charges inside or outside a dielectric sphere

Authors:
Wei Cai;Shaozhong Deng;Donald Jacobs
Affiliations:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States;Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States;Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

In this paper, we propose a novel method to extend the fast multipole method (FMM) to calculate the electrostatic potential due to charges inside or outside a dielectric sphere. The key result which allows such an extension is the construction of a small number (two for a 10^-^2 relative error in reaction potentials inside the sphere) of image point charges for source point charges inside or outside the dielectric sphere. Numerical results validate the accuracy and high efficiency of the resulting algorithm.