Development of a Massively Parallel Particle-Mesh Algorithm for Simulations of Galaxy Dynamics and Plasmas.
GEORGE MASON UNIV FAIRFAX VA
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Particle-mesh calculations treat forces and potentials as field quantities which are represented approximately on a mesh. A system of particles is mapped on to this mesh as a density distribution of mass or charge. The Fourier transform is used to convolve this distribution with the Greens 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 particle-particle methods computing time relies on direct summation, so the time for each calculation is given by Np2, where Np is the number of particles. The particle-mesh 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 two-body interactions are important. Particle mesh methods still dominate in plasma physics where collisionless systems are modeled. The CM-200 Connection Machine produced by Thinking Machines Corp. is a data parallel system. On this system, the front-end computer controls the timing and execution of the parallel processing units. The programming paradigm is Single-Instruction, Multiple Data SIMD. The processors on the CM-200 are connected in an N-dimensional 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.
- Plasma Physics and Magnetohydrodynamics