Load-Balancing and Performance of a Gridless Particle Simulation on MIMD, SIMD, and Vector Supercomputers

Our charged particle simulation models a relativistic electron beam for which the field solution is local and thus requires no grid. We have implemented the simulation on a CRAY and on two parallel machines, a nCUBE 2 and Connection Machine. We present implementation details and contrast the approaches necessary for the three architectures. On the parallel machines a dynamic load-balancing problem arises because the beam grows uniformly in one dimension from a few hundred to hundreds of thousands of particles as the simulation progresses. We discuss a folded Gray-code mapping of the processors to the length scale of the simulation that expands (or shrinks) as the beam changes length so as to minimize inter-processor communication. This improves the efficiency of the nCUBE version of the simulation which runs at 10x the speed of the vectorized CRAY version.