Materials Science Study by Molecular Dynamics


1. Method

When we study high-temperature plasmas and the microscopic
structure and functionality of condensed matters by computer
simulations, we use either classical molecular dynamics code
based on Newtonian dynamics, or the first principle code based
on quantum mechanics, depending on the scale and the process
to be studied. The former code can deal with the stellar motions
in the universe down to atomic motions in nanometer scales.
The latter code should be used for the study that includes atomic
processes where overlapping of atoms, hence that of electron
orbits, takes place.

　The electrostatic forces are inverse-square forces like the
gravitational forces, which are long-range forces in nature. But,
one has to calculate them correctly also for short distances since
particle near-by collisions are frequent. Thus, we take summation
of the short-range part of the electrostatic forces over all the ion
combinations. This requires N*N calculations on each time step
of the simulation run, where N is the number of ions in the system.
If we integrate the equations for, at least, 100,000 steps and with
N= 1000, the total of 100 billion calculations are executed in the
run. Thus, we must use a fast computer for molecular dynamics
simulations.

　In the classical molecular dynamics, the most time consuming
part of computation is the Ewald sum which takes into account
the periodicity of the charge distribution（typical in crystals).　
However, the equations are rather simple. By contrast, the
first-principle molecular dynamics code solves the equation for
electron density, which requires large matrix diagonalization.
These procedures are rather complicated and even heavier in
computation than solving equations of motion.

2. PC Cluster Machines

As explained above, molecular dynamics simulations need
very fast computers, and only supercomputers could do the job
before. Now, the x86-based PC cluster machines are replacing
conventional supercomputers bacuase of their capability
of handling large amount of computations. Thus, if one can
wisely parallelize the molecular dynamics code, a Boewulf PC
cluster (parallel computer) is highly suited for molecular
dynamics simulations.

　For these reasons, we constructed several clusters based on
Pentium III (1GHz), Xeon (2.4GHz), Pentium 4 (3GHz) with
MPICH. We found later that using the low-latency communication
software GAMMA doubles the computation power.
　Recently we use Opteron 2.8 GHz clusters with the SuSE
Linux ES and the InfiniBand MPI for inter-processor communications.
We are making good use of these cluster machines in our current
research of plasma and condensed matters.


Topics
Boewulf PC cluster: How to make and use it (summary)

Our Boewulf PC Cluster Machine　(report)

Xeon Processors and Remarks May 2003

Performance of Pentium 4 Processors Oct. 2003


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