Harmonic Analysis and Applications

June 4-8, 2018


"The P2NFFT method for mixed charge-dipole systems"

Nestler, Franziska

We consider a typical $N$-body problem in order to compute electrostatic interactions in particle systems containing a mixture of charges and dipoles. Classical particle-mesh methods make use of the fast Fourier transform (FFT) to compute the interactions in pure charge systems subject to periodic boundary conditions in all three spatial directions. This enables the approximation of the desired quantities with only $\mathcal O(N\log N)$ arithmetic operations, where $N$ denotes the number of present charges. Particle systems containing a set of dipoles have already been studied as well and may be treated in a similar fashion. One particle-mesh method is called the particle-particle NFFT (P$^2$NFFT), which is based on the nonuniform fast Fourier transform (NFFT). Recently, this method has been generalized to 2d-periodic, 1d-periodic as well as open boundary conditions. In addition, the approach has been extended for the treatment of particle systems containing a mixture of charges and dipoles. Consequently, we present for the first time an efficient $\mathcal O(N\log N)$ algorithm for mixed charge-dipole systems, that in addition allows the handling of various types of periodic boundary conditions based on a unified framework. The method is publicly available. Numerical results confirm that the method can be tuned to high accuracies.

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