A Fast Method for Evaluating Green's Function in Irregular Domains with Application to Charge Interaction in a Nanopore (Communications in Computational Physics, 2020)
We develop a fast meshless algorithm for electrostatic interaction in an irregulardomain with given potential boundary conditions, which is of importance inmany applications such as electrochemical energy and electric structure calculations.The algorithm is based on an approximation of the Green's function using two-levelimage charges, in which the inner-layer charges are located nearby the boundary toeliminate the singularity of the induced polarization potential, and the outer-layercharges with fixed positions approximate the long-range tail of the potential. We findthe number of inner-layer image charges can be very small and thus the total complexityof the algorithm is less expensive and potentially suitable for use in particlesimulations. The numerical results show the performance of the algorithm is attractive.We also use the algorithm to investigate the electrostatic interaction for particlesin a cylindrical nanopore and show that the electrostatic interaction within the porehas an exponential decay.
Keywords: Poisson's equation; image charge methods; meshless algorithm; electrostatic many-body phenomena; Green's function.