We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using Ewald splitting to replace the original Poisson equation for nearly-singular sources with a smooth far-field Poisson equation, combined with a localized near-field correction. Unlike existing spectral Ewald methods, which make use of the Fourier transform in the aperiodic direction, we recast the problem as a two-point boundary value problem in the aperiodic direction for each transverse Fourier mode, for which exact analytic boundary conditions are available. We solve each of these boundary value problems using a fast, well-conditioned Chebyshev method. In the presence of dielectric jumps, combining Ewald splitting with the classical method of images results in smoothed charge distributions which overlap the dielectric boundaries themselves. We show how to preserve high order accuracy in this case through the use of a harmonic correction which involves solving a simple Laplace equation with smooth boundary data. We implement our method on Graphical Processing Units, and combine our doubly-periodic Poisson solver with Brownian Dynamics to study the equilibrium structure of double layers in binary electrolytes confined by dielectric boundaries. Consistent with prior studies, we find strong charge depletion near the interfaces due to repulsive interactions with image charges, which points to the need for incorporating polarization effects in understanding confined electrolytes, both theoretically and computationally.
翻译:我们开发了一种快速的方法,用来计算静电能量和电力,以收集在平板边界的双周期性平板的收费。我们的方法通过使用Ewald分解来取代原Poisson等式,以平滑的远野Poisson等式取代近色源的原始Poisson等式,加上局部的近地校正。与现有的光谱Ewald方法不同,它利用Fourier变换周期性方向,我们把问题缩小为两点边界值问题,在每个跨向的Fourier模式的周期性方向中,以跳跃式平流电流通电路,我们的方法实现了光度平流的平板边界结构,我们用直流的平流平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面,我们用平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面,我们平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平平