A fast algorithm for particle simulations
Journal of Computational Physics
The electric potential of a macromolecule in a solvent: A fundamental approach
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
Journal of Computational Physics
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Extending the fast multipole method to charges inside or outside a dielectric sphere
Journal of Computational Physics
"New-version-fast-multipole-method" accelerated electrostatic calculations in biomolecular systems
Journal of Computational Physics
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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A recent article by Deng and Cai introduced fourth-order image approximations to the reaction field for a charge inside a dielectric sphere immersed in a solvent of low ionic strength (J. Comput. Phys. 227:1246---1266, 2007). To represent such a reaction field, the image approximations employ a point charge at the classical Kelvin image point and two line charges that extend from the Kelvin image point along the radial direction to infinity. In this paper, a sixth-order image approximation is developed, using the same point charge with three different line charges. Procedures on how to discretize the line charges by point image charges and how to implement the resulting point image approximation in O(N) complexity for potential and force field calculations are included. Numerical results demonstrate the sixth-order convergence rate of the image approximation and the O(N) complexity of the fast implementation of the point image approximation.