Fast Ewald summation based on NFFT with mixed periodicity

In this paper we develop new fast Fourier-based methods for the Coulomb problem. We combine the Ewald summation formulas and the fast summation approach based on the nonequispaced fast Fourier transform (NFFT) in order to develop efficient methods for calculating the Coulomb energies as well as the acting forces in charged particle systems subject to mixed periodic boundary conditions. Therewith, we extend the applicability of NFFT based methods, which already exist for open as well as for 3d-periodic boundary conditions, to arbitrary combinations of periodic and open boundary conditions. We reconsider the derivation of the Ewald formulas for 2d- and 1d-periodic systems, introduce the new algorithms and present high precision numerical results.