  We develop a new Lagrangian material particle -- dynamical domain
decomposition method (MPD^3) for large scale parallel molecular dynamics (MD)
simulation of nonstationary heterogeneous systems on a heterogeneous computing
net. MPD^3 is based on Voronoi decomposition of simulated matter. The map of
Voronoi polygons is known as the Dirichlet tessellation and used for grid
generation in computational fluid dynamics. From the hydrodynamics point of
view the moving Voronoi polygon looks as a material particle (MP). MPs can
exchange particles and information. To balance heterogeneous computing
conditions the MP centers should be dependent on timing data. We propose a
simple and efficient iterative algorithm which based on definition of the
timing-dependent balancing displacement of MP center for next simulation step.
  The MPD^3 program was tested in various computing environments and physical
problems. We have demonstrated that MPD^3 is a high-adaptive decomposition
algorithm for MD simulation. It was shown that the well-balanced decomposition
can result from dynamical Voronoi polygon tessellation. One would expect the
similar approach can be successfully applied for other particle methods like
Monte Carlo, particle-in-cell, and smooth-particle-hydrodynamics.
