Implementation of non-uniform FFT based Ewald summation in Dissipative Particle Dynamic method

The ENUF method, i.e., Ewald summation based on the Non-Uniform FFT technique (NFFT), is implemented in Dissipative Particle Dynamics (DPD) simulation scheme to fast and accurately calculate the electrostatic interactions at mesoscopic level. In a simple model electrolyte system, the suitable ENUF-DPD parameters, including the convergence parameter $\alpha$, the NFFT approximation parameter $p$, and the cut-offs for real and reciprocal space contributions, are carefully determined. With these optimized parameters, the ENUF-DPD method shows excellent efficiency and scales as $\mathcal{O}(N\log N)$. The ENUF-DPD method is further validated by investigating the effects of charge fraction of polyelectrolyte, ionic strength and counterion valency of added salts on polyelectrolyte conformations. The simulations in this paper, together with a separately published work of dendrimer-membrane complexes, show that the ENUF-DPD method is very robust and can be used to study charged complex systems at mesoscopic level.