Fast Ewald summation for electrostatic potentials with arbitrary periodicity

Understand

A unified treatment for fast and spectrally accurate evaluation of electrostatic potentials subject to periodic boundary conditions in any or none of the three spatial dimensions is presented.

• Ewald decomposition is used to split the problem into a real-space and a Fourier-space part, and the FFT-based Spectral Ewald (SE) method is used to accelerate the computation of the latter.
• A key component in the unified treatment is an FFT-based solution technique for the free-space Poisson problem in three, two or one dimensions, depending on the number of non-periodic directions.
• The computational cost is furthermore reduced by employing an adaptive FFT for the doubly and singly periodic cases, allowing for different local upsampling factors.