================================================================== === === === GENESIS Distributed Memory Benchmarks === === === === MD1 === === === === Molecular Dynamics for a Lennard Jones fluid - 3D ver. === === === === Versions: Std F77, PARMACS, Subset HPF === === === === Author: Mark Pinches === === Subset HPF: Bryan Carpenter === === Department of Electronics and Computer Science === === University of Southampton === === Southampton SO9 5NH, U.K. === === fax.:+44-703-593045 e-mail:mrsp@uk.ac.soton.pac === === dbc@uk.ac.soton.ecs === === === === Last update: May 1993; Release: 2.2 === === === ================================================================== 1. Description -------------- Molecular dynamics essentially involves solution of the equations of motion for a system of a large number of interacting particles, i.e. solving second order differential equations. The problem is solved numerically by calculating approximate solutions at a large number of time steps with interval dt, where dt is small in comparison with the time taken for a molecule with average velocity to travel a typical interatomic distance. The particles are usually considered to interact through an effective pair potential which is often adjusted to reproduce experimental results and is used to model the exact many-body potential. For monatomic neutral atoms the form of pair potential most often employed is the Lennard-Jones potential, which is characterised by a steep repulsive term and a long-range tail. When modelling homogeneous bulk phases, periodic boundary conditions are usually applied, so the `box' containing the system to be studied can be considered to be replicated by an infinite `lattice'. A typical MD calculation for N particles involves, for each time step: - calculating the forces on the N particles; - calculating their new positions; - calculating properties of interest, such as energies and radial distribution functions. In addition, diagnostic output and perhaps particle coordinates (the latter involving a large amount of output for large systems) may be required at intervals of tens or hundreds of time steps. A simulation usually proceeds in two phases: - Equilibration - the atoms in an initially static lattice are given random velocities, sampled from a Gaussian distribution scaled to give the correct temperature, and an equilibrium (i.e. minimum free energy) configuration is determined by running the simulation, rescaling the kinetic energies at each timestep to maintain the required temperature. - Simulation - the coordinates from the previous step are used in a simulation, run at constant energy, from which information on the system being studied is produced. The period of this simulation must be sufficient to obtain good statistical averages of the required properties. For many systems, the number of terms can be limited because the short range nature of the Lennard-Jones potential means that reasonable accuracy can be obtained by considering only atom pairs with interatomic distances within a cutoff range, which is of the order of a few atomic diameters. Long range corrections are used in the calculation of thermodynamic properties. For small systems this strategy is sufficient to ensure that the forces are evaluated efficiently. For large systems, however, the number of interatomic terms required to evaluate the force is small compared with the total number of atom pairs, and the time taken to decide whether the separation of a given pair is less than r_{c} is itself highly significant. An algorithm has been developed by Hockney et al, the linked-list algorithm, which minimises the time taken to find atomic pairs that contribute significantly to the potential. This algorithm subdivides the system into a number of cells, which may be 1, 2 or 3 dimensional. Cubic cells are the most appropriate for large bulk systems. At each timestep each atom is allocated to a cell, and one atom from each cell is selected as the first atom in that cell. Provided that the cell size is chosen properly, the interatomic distances need only be calculated for atoms in the current and nearest neighbour cells. Note however that for edge and corner cells, those at the opposite edges and corners are involved because of the periodic boundary conditions. Implementation of this algorithm on a parallel machine involves the allocation of a number of adjacent cells to one processor. Cells at the edges and corners of the processor must communicate with neighbouring processors and each cell must communicate with a `driver' which is responsible for input/output and supervision of the process, which is synchronised once per timestep. 2. Operating instructions ------------------------- Changing problem size and numbers of processes: Most of the parameters are internally fixed for the case of the gas Krypton. The user has to specify only the number of processors in each direction and the number of latice cells NC, which will result in 4*NC*NC*NC atoms. These are read from the standard input on channel 5. Suggested Problem Sizes : For realistic simulation at least 2000 atoms per node is recommended, which means that NC**3 > 500*NP where NP is the total number of processors (NP = NPX*NPY*NPZ). This is in fact the limit for the smallest possible problem size. The upper limit depends on the amount of local memory. Compiling and running the benchmark: 1) To compile and link the benchmark type: `make' for the distributed version or `make slave' for the single-node version. 2) To run either sequential or distributed version of the benchmark, type: md1 3) Input parameters NPX, NPY, NPZ and NC (see above) on standard input. Output from the benchmark is written to the file "result" 3. Accuracy check ----------------- After the equilibration phase the total energy should be conserved, i.e. the first few digits should remain constant and there should certainly be no net drift in the values. The temperature should not vary by more than 0.1 if the simulation is to produce sensible simulation data. If it does, the equilibration time has to be increased by increasing the number of equilbration steps, NEQUIL, in the host-program. $Id: ReadMe,v 1.2 1994/04/20 17:41:15 igl Rel igl $

Submitted by Mark Papiani,

last updated on 10 Jan 1995.