In this work, we upgraded the electrostatic interaction method of CU-ENUF (Yang, et al., 2016) which first applied CUNFFT (nonequispaced Fourier transforms based on CUDA) to the reciprocal-space electrostatic computation and made the computation of electrostatic interaction done thoroughly in GPU. The upgraded edition of CU-ENUF runs concurrently in a hybrid parallel way that enables the computation parallelizing on multiple computer nodes firstly, then further on the installed GPU in each computer. By this parallel strategy, the size of simulation system will be never restricted to the throughput of a single CPU or GPU. The most critical technical problem is how to parallelize a CUNFFT in the parallel strategy, which is conquered effectively by deep-seated research of basic principles and some algorithm skills. Furthermore, the upgraded method is capable of computing electrostatic interactions for both the atomistic molecular dynamics (MD) and the dissipative particle dynamics (DPD). Finally, the benchmarks conducted for validation and performance indicate that the upgraded method is able to not only present a good precision when setting suitable parameters, but also give an efficient way to compute electrostatic interactions for huge simulation systems. Program summary Program title: HP-ENUF Program Files doi: http://dx.doLorg/10.17632/zncf24thpv.1 Licensing provisions: GNU General Public License 3 (GPL) Programming language: C, C++, and CUDA C Supplementary material: The program is designed for effective electrostatic interactions of large-scale simulation systems, which runs on particular computers equipped with NVIDIA CPUs. It has been tested on (a) single computer node with Intel(R) Core(TM) i7-3770@ 3.40 GHz (CPU) and GTX 980 Ti (GPU), and (b) MPI parallel computer nodes with the same configurations. Nature of problem: For molecular dynamics simulation, the electrostatic interaction is the most time-consuming computation because of its long-range feature and slow convergence in simulation space, which approximately take up most of the total simulation time. Although the parallel method CU-ENUF (Yang et al., 2016) based on GPU has achieved a qualitative leap compared with previous methods in electrostatic interactions computation, the computation capability is limited to the throughput capacity of a single GPU for super scale simulation system. Therefore, we should look for an effective method to handle the calculation of electrostatic interactions efficiently for a simulation system with super-scale size. Solution method: We constructed a hybrid parallel architecture, in which CPU and GPU are combined to accelerate the electrostatic computation effectively. Firstly, the simulation system is divided into many subtasks via domain-decomposition method. Then MPI (Message Passing Interface) is used to implement the CPU parallel computation with each computer node corresponding to a particular subtask, and furthermore each subtask in one computer node will be executed in GPU in parallel efficiently. In this hybrid parallel method, the most critical technical problem is how to parallelize a CUNFFT (nonequispaced fast Fourier transform based on CUDA) in the parallel strategy, which is conquered effectively by deep-seated research of basic principles and some algorithm skills. Restrictions: The HP-ENUF is mainly oriented to super-scale system simulations, in which the performance superiority is shown adequately. However, for a small simulation system containing less than 106 particles, the mode of multiple computer nodes has no apparent efficiency advantage or even lower efficiency due to the serious network delay among computer nodes, than the mode of single computer node. References: (1) S.-C. Yang, H.J. Qian, Z.-Y. Lu, Appl. Comput. Harmon. Anal. 2016, http://dx.doLorg/10.1016/j.acha. 2016.04.009. (2) S.-C. Yang, Y.-L. Wang, G.-S. Jiao, H.J. Qian, Z.-Y. Lu, J. Comput. Chem. 37 (2016) 378. (3) S.-C. Yang, Y.-L. Zhu, H.-J. Qian, Z.-Y. Lu, Appl. Chem. Res. Chin. Univ., 2017, http://dx.doi.org/10.1007/ s40242-016-6354-5. (4) Y.-L. Zhu, H. Liu, Z.-W. Li, H.J. Qian, G. Milano, Z.-Y. Lu, J. Comput. Chem. 34 (2013) 2197. (C) 2017 Elsevier B.V. All rights reserved.
