Michael Hofmann, Franziska Nestler, Michael Pippig: NFFT based Ewald summation for electrostatic systems with charges and dipoles

Author(s):

Michael Hofmann
Franziska Nestler
Michael Pippig

Title:

Michael Hofmann, Franziska Nestler, Michael Pippig: NFFT based Ewald summation for electrostatic systems with charges and dipoles

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 07, 2016

Mathematics Subject Classification:

    65T []

Abstract:

The efficient computation of Coulomb interactions in charged particle systems is of great importance in the field of molecular dynamics simulations. It is widely known that an approximation can be realized based on the Ewald summation approach and the fast Fourier transform (FFT). In the present paper we consider particle systems containing a mixture of $N$ point charges as well as point dipoles. The cutoff errors in the Ewald summation formulas are derived and validated by numerical examples. Furthermore, we present for the first time an $\mathcal O(N\log N)$ algorithm for computing mixed charge--dipole interactions based on the FFT for nonequispaced data (NFFT). Thereby the treatment of pure charge and pure dipole systems is also covered as a special case. Our novel approach can be understood as a new module within the particle-particle NFFT (P$^2$NFFT) framework. Therefore our proposed charge-dipole algorithms can be combined with all the formerly derived P$^2$NFFT features, which cover for instance the treatment of arbitrary combinations of periodic and non-periodic boundary conditions, the handling of triclinic box shapes and a massively parallel implementation. In order to calculate the interactions with dipoles efficiently, two new variants of the NFFT, namely the Hessian NFFT as well as the adjoint gradient NFFT, are derived and implemented. In the context of NFFT, these new variants are of great importance on their own. The described method can be tuned to a high precision and is publicly available as a part of the ScaFaCoS library.

Keywords:

Ewald summation, nonequispaced fast Fourier transform, particle methods, charged particle systems, dipole-dipole interactions, charge-dipole interactions, periodic boundary conditions, NFFT, P2NFFT, P3M, ScaFaCoS

Language:

English

Publication time:

11/2016