A Robust Numerical Method for Generalized Coulomb and Self-Polarization Potentials of Dielectric Spheroids
Changfeng Xue 1, Shaozhong Deng 2*1 Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng, Jiangsu 224003, China.
2 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.
Received 4 October 2009; Accepted (in revised version) 30 November 2009
Available online 12 March 2010
By utilizing a novel quasi-harmonic three-layer dielectric model for the interface between a dielectric spheroid and the surrounding dissimilar dielectric medium, a robust numerical method for calculating the generalized Coulomb and self-polarization potentials of the dielectric spheroid is presented in this paper. The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest step-like model of the dielectric interface, but also completely eliminate the potential numerical divergence which may occur in other treatments. Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a general three-layer dielectric model goes to infinity.
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PACS: 41.20.Cv, 73.21.La, 87.15.A-
Key words: Generalized Coulomb potential, self-polarization potential, quantum dot, hybrid solvation model, Poisson equation.
Email: firstname.lastname@example.org (C. Xue), email@example.com (S. Deng)