A flexible algorithm for calculating pair interactions on SIMD architectures

Abstract

Calculating interactions or correlations between pairs of particles is typically the most time-consuming task in particle simulation or correlation analysis. Straightforward implementations using a double loop over particle pairs have traditionally worked well, especially since compilers usually do a good job of unrolling the inner loop. In order to reach high performance on modern CPU and accelerator architectures, singleinstruction multiple-data (SIMD) parallelization has become essential. Avoiding memory bottlenecks is also increasingly important and requires reducing the ratio of memory to arithmetic operations. Moreover, when pairs only interact within a certain cut-off distance, good SIMD utilization can only be achieved by reordering input and output data, which quickly becomes a limiting factor. Here we present an algorithm for SIMD parallelization based on grouping a fixed number of particles, e.g. 2, 4, or 8, into spatial clusters. Calculating all interactions between particles in a pair of such clusters improves data reuse compared to the traditional scheme and results in a more efficient SIMD parallelization. Adjusting the cluster size allows the algorithm to map to SIMD units of various widths. This flexibility not only enables fast and efficient implementation on current CPUs and accelerator architectures like GPUs or Intel MIC, but it also makes the algorithm future-proof. We present the algorithm with an application to molecular dynamics simulations, where we can also make use of the effective buffering the method introduces.

Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS

“…17 First, the particles are placed on a grid in the x and y dimensions, and then binned in the z dimension. This efficiently groups particles that are close in space, and permits the construction of a list of clusters, each containing exactly M particles.…”

Relative Orientation of POTRA Domains from Cyanobacterial Omp85 Studied by Pulsed EPR Spectroscopy

“…A 5 fs time step was enabled by converting hydrogen atoms to virtual sites (pdb2gmx option -vsite hydrogens). The Verlet cutoff scheme was used for neighbor searching (58). The short-range cutoff was 1.4 nm.…”

Direct-Space Corrections Enable Fast and Accurate Lorentz–Berthelot Combination Rule Lennard-Jones Lattice Summation

“…The simulations were performed using the new Verlet cutoff scheme (later referenced as Verlet scheme) in Gromacs. 32 The DPPC bilayer, containing 400 DPPC molecules and 12,820 SPC/E water molecules, was constructed replicating our previous DPPC-system 18 first along the x-and then along the y-axis making it four times larger. The system was first equilibrated using a conjugate gradient method with the tolerance 1 kJ mol −1 nm −1 , followed by an MD simulation using a timestep of 0.2 fs for 30,000 steps after which the time step was increased to 2 fs and an additional 30,000 steps were performed.…”