Franziska Nestler: An NFFT based approach to the efficient computation of dipole-dipole interactions under different periodic boundary conditions

Author(s):

Franziska Nestler

Title:

Franziska Nestler: An NFFT based approach to the efficient computation of dipole-dipole interactions under different periodic boundary conditions

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 07, 2015

Mathematics Subject Classification:

    65T []

Abstract:

We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.

Keywords:

Ewald summation, nonequispaced fast Fourier transform, particle methods, dipole-dipole interactions, mixed periodicity, NFFT, P2NFFT, P3M

Language:

English

Publication time:

05/2015