A fast spectral method for electrostatics in doubly periodic slit channels

We develop a fast method for computing the electrostatic energy and forces collection of charges in doubly-periodic slabs with jumps dielectric permittivity at slab boundaries. Our achieves spectral accuracy by using Ewald splitting to replace original Poisson equation nearly-singular sources smooth far-field equation, combined localized near-field correction. Unlike existing methods, which make use Fourier transform aperiodic direction, we recast problem as two-point boundary value direction each transverse mode, exact analytic conditions are available. solve these problems fast, well-conditioned Chebyshev method. In presence jumps, combining classical images results smoothed charge distributions overlap boundaries themselves. show how preserve this case through harmonic correction involves solving simple Laplace data. implement our on Graphical Processing Units, combine solver Brownian Dynamics study equilibrium structure double layers binary electrolytes confined Consistent prior studies, find strong depletion near interfaces due repulsive interactions image charges, points need incorporating polarization effects understanding electrolytes, both theoretically computationally.