Kaiser-Bessel Basis for the Particle-Mesh Interpolation

TL;DR

This paper introduces the Kaiser-Bessel basis for particle-mesh interpolation in the fast Ewald method, providing a new approach that improves accuracy over traditional B-spline bases through optimized parameters and error estimation.

Contribution

The paper develops a reliable a priori error estimate and demonstrates that the Kaiser-Bessel basis can outperform B-spline bases in accuracy for particle-mesh interpolations.

Findings

Kaiser-Bessel basis achieves higher accuracy than B-spline basis in certain parameter regimes.

Optimized shape parameter improves force computation accuracy.

Kaiser-Bessel basis can be over ten times more accurate in some cases.

Abstract

In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated charge systems, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional B-spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, saying a relatively small real space cutoff, a relatively small reciprocal space mesh and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate.