A massively parallel particle-in-cell technique for a three-dimensional simulation of plasma phenomena
Saleh H. Al-Sharaeh, B. Earl Wells · 1996
In this work, a new multiple-instruction-multiple-data restructuring technique has been developed which can be used to parallelize large three-dimensional simulations of plasma phenomena. This technique is designed to effectively exploit the data parallelism present within these simulations and produces parallel representations which execute over a wide variety of parallel processing environments including multicomputers, clusters of workstations, and massively parallel systems which possess distributed shared memory. The technique combines static allocation methodologies, where the problem is partitioned in a manner which is based upon the physical geometry of the simulation space, with dynamic load balancing techniques, which can be used to effectively alter the partitioning at run time by examining the degree to which plasma particle movement has caused the processing load to become unbalanced. The technique exploits the fact that the desired simulation volume is often elongated around a single dimension and that the simulation space is assumed to be periodic. The natural topology for such simulations is therefore ring-like in structure, leading to a generic representation which can be effectively mapped onto multiple parallel processing configurations by employing embedding algorithms based upon base-2 reflected Gray encoding. The restructuring technique has been analyzed empirically and analytically to determine how well such simulations can be expected to perform as the geometric domain of the simulation increases in size (and/or the number of particles per cell increases) as the number of processors is increased. From this analysis, it has been determined that though the methodology does not appear to have outstanding asymptotic scalability properties, it exhibits near fixed-time scalability for the problem sizes and parallel computer configurations that are likely to be considered in the foreseeable future. As part of this research, the proposed parallel restructuring technique has been repetitively applied to investigate the nonlinear evolution of the lower hybrid waves in the Auroral region of the Earth's ionosphere. This problem was selected because a better understanding of it will aid in the prediction of space weather which in turn will allow for the better protection of humans and electronic equipment from the effects of geomagnetic disturbances. Initial results support the lower hybrid wave collapse theory. Furthermore, the results show that the lower hybrid waves indirectly initiate the acceleration of the cold plasma by parametrically driving secondary waves with slow phase velocities suited for the transverse acceleration of ions and parallel acceleration of electrons. This process produces electron and ion populations having features as measured in rocket experiments. The restructuring technique has been used successfully to map this problem onto an nCUBE/2 multicomputer, a cluster of heterogeneous SUN workstations, and a 256 node Cray T3D massively parallel processor. The efficiency of these implementations was shown to be very high (greater than 96% for nCUBE/2 and Cray T3D) with the best implementation outperforming similar simulations run on a Cray C-90 by a factor of $\sim$333.