ENUF, an abbreviation for the Ewald summation method based on Non-Uniform fast Fourier transform (NFFT) technique, is a method proposed to calculate electrostatic interactions between charged particles in molecular simulation systems.

The ENUF method was first implemented in the classic molecular dynamics simulation code, and thereafter in the dissipative particle dynamics (DPD) framework to calculate electrostatic interactions between charge density distributions at mesoscopic level. Selecting a set of optimal physical parameters, the ENUF method gives a good precision as desired and bears a computational complexity of O(NlogN), which is comparable to that of PME (particle-mesh Ewald summation method) and PPPM (particle-particle particle-mesh Ewald summation method) methods.

The ENUF and ENUF-DPD methods were adopted to explore the dependence of conformational properties of polyelectrolytes on charge fraction, ion concentration and counterion valency of added salts, to investigate specific binding structures of dendrimers on bilayer membranes and the corresponding permeation mechanisms, and to study heterogeneous structures and dynamics in ionic liquids and how electrostatic interactions between charged particles affect these properties at extended spatiotemporal scales.

This folder contains the code (serial version) to simulate properties of ions in aqueous dilute solution. The code is written using Fortran and C. The FFTW library should be installed before compilation of the source code.

This folder contains the paralled version of the code to simulate properties of ions in aqueous dilute solution. The code is written using Fortran and C and paralleled using MPI.

This folder contains several files that have been implemented in the GALAMOST package. The descriptions of these methods are available in Ref. [5].

This folder contains files for the publication 7 including two parts: the source code and the input data for the validation of the proposed computational scheme.

• cunfft.cu is used to transfer input data from host (CPU) to device (GPU), compute NDFT in device, and thereafter fetch computational results from device to host. cunfft.h is the relelatd head file.
• util.c and util.h are used for benchmark
• Makefile contains commands for the hybrid CUDA-MPI compilation scheme, and an executable file named CUDA_MPI_TEST will be available after the correct compilation

[1] Y.-L. Wang, A. Laaksonen*, Z.-Y. Lu*. Implementation of non-uniform FFT based Ewald summation in dissipative particle dynamics method. J. Comput. Phys. 235, 666-682 (2013).

[2] Y.-L. Wang, F. Hedman, M. Porcu, F. Mocci, A. Laaksonen*. Non-uniform FFT and its applications in particle simulations, Applied Mathematics 5, 520-541 (2014).

[3] S.-C. Yang, Y.-L. Wang, G.-S. Jiao, H.-J. Qian*, Z.-Y. Lu. Accelerating electrostatic interaction calculations with graphical processing units based on new developments of Ewald method using non-uniform fast Fourier transform, J. Comput. Chem. 37, 378-387 (2016).

[4] S.-C. Yang*, Z.-Y. Lu, H.-J. Qian, Y.-L. Wang, J.-P. Han. A hybrid Parallel architecture for electrostatic interactions in simulation of dissipative particle dynamics. Comput. Phys. Commun. 220, 376-389 (2017).

[5] Y.-L. Wang∗, Y.-L. Zhu, Z.-Y. Lu, A. Laaksonen*. Electrostatic interactions in soft particle systems: Mesoscale simulations of ionic liquids, Soft Matter 14, 4252-4267 (2018) (Highlighted on the inside back cover of Soft Matter).

[6] S.-C. Yang, B. Li, Y.-L. Zhu, A. Laaksonen, Y.-L. Wang*, The ENUF method –- Ewald summation based on non-uniform fast Fourier transform: Implementation, parallelization, and application, J. Comput. Chem. 41, 2316-2335 (2020).

[7] S.-C. Yang, Y.-L. Wang*. A hybrid MPI-CUDA approach for nonequispaced discrete Fourier transformation, Comput. Phys. Commun. 258, 107513 (2021).