Development of a Massively Parallel ParticleMesh Algorithm for Simulations of Galaxy Dynamics and Plasmas
Abstract
Particlemesh calculations treat forces and potentials as field quantities which are represented approximately on a mesh. A system of particles is mapped onto this mesh as a density distribution of mass or charge. The Fourier transform is used to convolve this distribution with the Green's function of the potential, and a finite difference scheme is used to calculate the forces acting on the particles. The computation time scales as the Ng log Ng, where Ng is the size of the computational grid. In contrast, the particleparticle method's computing time relies on direct summation, so the time for each calculation is given by Np2, where Np is the number of particles. The particlemesh method is best suited for simulations with a fixed minimum resolution and for collisionless systems, while hierarchical tree codes have proven to be superior for collisional systems where twobody interactions are important. Particle mesh methods still dominate in plasma physics where collisionless systems are modeled. The CM200 Connection Machine produced by Thinking Machines Corp. is a data parallel system. On this system, the frontend computer controls the timing and execution of the parallel processing units. The programming paradigm is SingleInstruction, Multiple Data (SIMD). The processors on the CM200 are connected in an Ndimensional hypercube; the largest number of links a message will ever have to make is N. As in all parallel computing, the efficiency of an algorithm is primarily determined by the fraction of the time spent communicating compared to that spent computing. Because of the topology of the processors, nearest neighbor communication is more efficient than general communication.
 Publication:

George Mason Univ. Technical Report
 Pub Date:
 January 1996
 Bibcode:
 1996gmu..rept.....W
 Keywords:

 Galaxies;
 Space Plasmas;
 Computerized Simulation;
 Computational Grids;
 Parallel Processing (Computers);
 Plasma Physics;
 Algorithms;
 Fourier Transformation;
 Functions (Mathematics);
 Finite Difference Theory;
 Massively Parallel Processors;
 Simd (Computers);
 Density Distribution;
 Astrophysics