Linked Cell Traversal Algorithms for Three-Body Interactions in Molecular Dynamics

TL;DR

The paper addresses the computational burden of non-additive three-body forces in molecular dynamics by introducing a parallel framework based on linked-cell traversals. It formalizes a general, cell-centered scheme that partitions triplet computations into one-, two-, and three-cell cases around a base cell and provides three traversal algorithms (3c01, 3c18, 3c08) with various levels of Newton's third law enforcement and neighborhood scope. The authors validate the approach using Lennard-Jones fluids in both homogeneous and inhomogeneous settings and assess performance with strong scalability metrics, highlighting trade-offs between accuracy and workload via pairwise and product cutoff conditions. The results demonstrate scalable three-body force calculations and reveal that optimized traversals can achieve significant performance gains while maintaining agreement in thermodynamic properties, enabling more accurate MD simulations of complex fluids and interfacial phenomena.

Abstract

In this work, algorithms for the parallel computation of three-body interactions in molecular dynamics are developed. While traversals for the computation of pair interactions are readily available in the literature, here, such traversals are extended to allow for the computation between molecules stored across three cells. A general framework for the computation of three-body interactions in linked cells is described, and then used to implement the corresponding traversals. In addition, our analysis is combined with the commonly used cutoff conditions, because they influence the total workload of the computation of interactions. The combinations between traversals and truncation conditions are validated using the well-known Lennard-Jones fluid. Validation case studies are taken from the literature and configured into homogeneous and inhomogeneous scenarios. Finally, strong scalability and performance in terms of molecule updates are measured at node-level.

Figures (8)

• Figure 1: A molecular triplet is shown. The distances follow the convention $\vec{r}_{\alpha\beta}=\vec{r}_\alpha-\vec{r}_\beta$. The potential is defined in terms of the magnitudes of the relative distances.
• Figure 2: All valid triplets for the pairwise cutoff (red, inner area surrounded by segmented line) and product cutoff (blue, outer region surrounded by solid line) in the $xy$ plane for $r_c = 1$.
• Figure 3: The base cell, $C_b$, contains three molecules $i,j,k$ such that $N_b=3$, for which the total interactions are given by \ref{['eq:celltriplet']}.
• Figure 4: An atomic triplet is split between the base cell, $C_b$, and an immediate neighbor $C_{n1}$. It is first assumed that two molecules are stored in $C_b$, then this assumption is reversed to $C_{n1}$.
• Figure 5: The particle triple $i,j,k$ is split between the cell triplet $\left(C_b,C_{n1},C_{n2}\right)$. A routine must be used to find a valid cell triplet using the base pair $\left(C_b,C_{n1}\right)$.