Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems

TL;DR

This paper introduces a fast, spectrally accurate Ewald summation method for 2D-periodic electrostatic systems, improving computational efficiency and memory usage while simplifying parameter selection.

Contribution

It presents a novel spectral representation-based PME-type method for 2P Ewald sums, with significant improvements in speed, memory, and error decoupling.

Findings

O(N log N) computational complexity

Vastly reduced memory requirements

Simplified parameter selection process

Abstract

A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast PME-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.