The Replicated Data Strategy

The Replicated Data (RD) strategy [42] is one of several ways to achieve parallelisation in MD. Its name derives from the replication of the configuration data on each node of a parallel computer (i.e. the arrays defining the atomic coordinates $\mbox{$\underline{r}$}_{i}$, velocities $\mbox{$\underline{v}$}_{i}$ and forces $\mbox{$\underline{f}$}_{i}$, for all $N$ atoms $\{i: i=1,\dots,N\}$ in the simulated system, are reproduced on every processing node). In this strategy most of the forces computation and integration of the equations of motion can be shared easily and equally between nodes and to a large extent be processed independently on each node. The method is relatively simple to program and is reasonably efficient. Moreover, it can be ``collapsed'' to run on a single processor very easily. However the strategy can be expensive in memory and have high communication overheads, but overall it has proven to be successful over a wide range of applications. These issues are explored in more detail in [42,43].

Systems containing complex molecules present several difficulties. They often contain ionic species, which usually require Ewald summation methods [12,44], and intra-molecular interactions in addition to inter-molecular forces. These are handled easily in the RD strategy, though the SHAKE algorithm [13] requires significant modification [30].

The RD strategy is applied to complex molecular systems as follows:

1. Using the known atomic coordinates $\mbox{$\underline{r}$}_{i}$, each node calculates a subset of the forces acting between the atoms. These are usually comprised of:
   1. atom-atom pair forces (e.g. Lennard Jones, Coulombic etc.);
   2. non-rigid atom-atom bonds;
   3. valence angle forces;
   4. dihedral angle forces;
   5. improper dihedral angle forces.
2. The computed forces are accumulated in (incomplete) atomic force arrays $\mbox{$\underline{f}$}_{i}$ independently on each node;
3. The atomic force arrays are summed globally over all nodes;
4. The complete force arrays are used to update the atomic velocities and positions.

It is important to note that load balancing (i.e. equal and concurrent use of all processors) is an essential requirement of the overall algorithm. In DL_POLY_2 this is accomplished for the pair forces with an adaptation of the Brode-Ahlrichs scheme [22].