Parallelization issues and particle-in-cell codes
Anne Cathrine Elster · 1994
Everything should be made as simple as possible, but not simpler. Albert Einstein. The field of parallel scientific computing has concentrated on parallelization of individual modules such as matrix solvers and factorizers. However, many applications involve several interacting modules. Our analyses of a particle-in-cell code modeling charged particles in an electric field, show that these accompanying dependencies affect data partitioning and lead to new parallelization strategies concerning processor, memory and cache utilization. Our test-bed, a KSR1, is a distributed memory machine with a globally shared addressing space. However, most of the new methods presented hold generally for hierarchical and/or distributed memory systems. We introduce a novel approach that uses dual pointers on the local particle arrays to keep the particle locations automatically partially sorted. Complexity and performance analyses with accompanying KSR benchmarks, have been included for both this scheme and for the traditional replicated grids approach. The latter approach maintains load-balance with respect to particles. However, our results demonstrate it fails to scale properly for problems with large grids (say, greater than 128-by-128) running on as few as 15 KSR nodes, since the extra storage and computation time associated with adding the grid copies, becomes significant. Our grid partitioning scheme, although harder to implement, does not need to replicate the whole grid. Consequently, it scales well for large problems on highly parallel systems. It may, however, require load balancing schemes for non-uniform particle distributions. Our dual pointer approach may facilitate this through dynamically partitioned grids. We also introduce hierarchical data structures that store neighboring grid-points within the same cache-line by reordering the grid indexing. This alignment produces a 25% savings in cache-hits for a 4-by-4 cache. A consideration of the input data's effect on the simulation may lead to further improvements. For example, in the case of mean particle drift, it is often advantageous to partition the grid primarily along the direction of the drift. The particle-in-cell codes for this study were tested using physical parameters, which lead to predictable phenomena including plasma oscillations and two-stream instabilities. An overview of the most central references related to parallel particle codes is also given.