Franziska Nestler: Parameter tuning for the NFFT based fast Ewald summation

Author(s):

Franziska Nestler

Title:

Franziska Nestler: Parameter tuning for the NFFT based fast Ewald summation

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 05, 2015

Mathematics Subject Classification:

    65T []

Abstract:

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P$^2$NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. While typically B-splines are applied in the scope of particle mesh methods, we consider for the first time also an approximation by Bessel functions. We show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that if the parameters are tuned appropriately the Bessel window function can keep up with the B-spline window and is in many cases even the better choice with respect to computational costs.

Keywords:

Ewald summation, particle methods, nonequispaced fast Fourier transform, NFFT, P3M, P2NFFT, ScaFaCoS

Language:

English

Publication time:

03/2015