  Simulating charged many-body systems has been a computational demanding task
due to the long-range nature of electrostatic interaction. For the multi-scale
model of electrolytes which combines the strengths of atomistic/continuum
electrolyte representations, a harmonic surface mapping algorithm is developed
for fast and accurate evaluation of the electrostatic reaction potentials. Our
method reformulates the reaction potential into a sum of image charges for the
near-field, and a charge density on an auxiliary spherical surface for the
far-field, which can be further discretized into point charges. Fast multipole
method is used to accelerate the pairwise Coulomb summation. The accuracy and
efficiency of our algorithm, as well as the choice of relevant numerical
parameters are demonstrated in detail. As a concrete example, for charges close
to the dielectric interface, our method can improve the accuracy by two orders
of magnitudes compared to the Kirkwood series expansion method.
