A Fast Method for Evaluating Green's Function in Irregular Domains with Application to Charge Interaction in a Nanopore

Abstract

We develop a fast meshless algorithm for electrostatic interaction in an irregular domain with given potential boundary conditions, which is of importance in many applications such as electrochemical energy and electric structure calculations. The algorithm is based on an approximation of the Green's function using two-level image charges, in which the inner-layer charges are located nearby the boundary to eliminate the singularity of the induced polarization potential, and the outer-layer charges with fixed positions approximate the long-range tail of the potential. We find the number of inner-layer image charges can be very small and thus the total complexity of the algorithm is less expensive and potentially suitable for use in particle simulations. The numerical results show the performance of the algorithm is attractive. We also use the algorithm to investigate the electrostatic interaction for particles in a cylindrical nanopore and show that the electrostatic interaction within the pore has an exponential decay.