Pure and Applied Mathematics Quarterly

Volume 14 (2018)

Number 1

Special Issue: In Honor of Chi-Wang Shu

Guest Editors: Jian-Guo Liu and Yong-Tao Zhang

Accurate and efficient calculation of singular electrostatic potentials in charge-dielectric sphere systems

Pages: 87 – 129

DOI: https://dx.doi.org/10.4310/PAMQ.2018.v14.n1.a4


Caylah Retz (Department of Mathematics, University of North Carolina, Charlotte, N.C., U.S.A.)

Wei Cai (Department of Mathematics, Southern Methodist University, Dallas, Texas, U.S.A.)


In this paper we introduce an efficient and accurate boundary element method for computing the electrostatic potential in closely-packed charge and dielectric spheres. A subtraction de-singularization technique is used to remove the singular part of the potential where the primary Coulomb potential and reaction field (approximated by image charges) are removed from the electrostatic potential. Regularization technique for the Hadamard finite part integral is also introduced for the second kind integral equations. Numerical results for one and two spheres have validated the effectiveness of the proposed method where much higher accuracy for the singular potential can be obtained with coarse meshes at a much reduced computational cost for closely packed charge-sphere systems.


Poisson–Boltzmann equation, dielectric sphere, charge

2010 Mathematics Subject Classification

65R20, 65Z05, 78M25

The work of this research was supported by US Army Research Office (Grant No. W911NF-17-1-0368) and US National Science Foundation (Grant No. DMS-1802143).

Received 28 March 2018

Published 2 April 2019