Spectrally accurate Ewald summation for the Yukawa potential in two dimensions

TL;DR

This paper introduces a spectrally accurate Ewald summation method for the two-dimensional Yukawa potential, enabling efficient computation with error estimates for both periodic and free-space cases.

Contribution

It develops a novel Ewald decomposition for the 2D Yukawa potential and provides error estimates to optimize the spectral Ewald method's parameters.

Findings

Achieves O(N log N) computational complexity.

Provides accurate error estimates for sum truncation.

Demonstrates effectiveness in boundary integral methods.

Abstract

An Ewald decomposition of the two-dimensional Yukawa potential and its derivative is presented for both the periodic and the free-space case. These modified Bessel functions of the second kind of zeroth and first degrees are used e.g. when solving the modified Helmholtz equation using a boundary integral method. The spectral Ewald method is used to compute arising sums at O(N log N) cost for N source and target points. To facilitate parameter selection, truncation-error estimates are developed for both the real-space sum and the Fourier-space sum, and are shown to estimate the errors well.