Multidimensional particle codes: Their capabilities and limitations

Increasing the number of dimensions calls for significant changes in simulation techniques. Demand on computer time and space increases by orders of magnitude and hardware development affects the feasibility. Gridless and Fokker-Planck codes are possible in ID, but one needs grids and PIC codes in 2D and 3D. This imposes limits on Debye lengths, particle size and spacing, and on resolution. Non-spectral (local) E-M codes also suffer a Courant restriction on δt, in addition to the usual ω_p δt restriction. Spectral methods therefore have an advantage; they also permit convenient filtering, particle shaping and control of resolution. 2D and codes are well advanced and documented (4,5). 3D codes are in their infancy. Data management, rather than physics or numerical analysis, becomes the major problem (10). Machine-independent 3D codes are too limited in resolution and speed. Parallelism helps greatly but makes the 3D codes machine-dependent. A present-day limit is attempted in a 2*128**3 grid code for CRAYs which process ∼ 5 million particles in ∼ 2 minutes per time step. Layering is employed to break up the 3D problem into many 2D problems. Fields and particles are packed and buffered in and out of core. Diagnostics are limited by the large volume of information accumulated in a run. Results of runs with 3D codes have tended to show that the third dimension, treated as “ignorable” in 2D simulations, should not have been ignored. With the next generation of highly parallel multiprocessors (which, however, call for the abandonment of spectral and implicit methods) one may hope to do very realistic 3D simulations.