A general performance model for parallel sweeps on orthogonal grids for particle transport calculations

There is a growing need to accurately simulate physical systems whose evolutions depend on the transport of subatomic particles. It has long been recognized that the huge computational demands of the transport problemmean that practical solution times will be obtained only by the eÆcient utilization of parallel processing. For example, since estimates place the time devoted to particle transport in multi-physics simulations at 50-80 % of total execution time, paralleliz-ing deterministic particle transport calculations is an important problem in many applications targeted by the DOE's Accelerated Strategic Computing Initiative (ASCI). One common ap-proach to deterministic particle transport calculations is the discrete-ordinates method, whose most time consuming step is the transport sweep which involves multiple sweeps through the spatial grid, one for each direction of particle travel. The eÆcient parallel implementation of the transport sweeps is the key to parallelizing the discrete-ordinates method. The key contribution of this paper is the rst general model which can be used to predict the running time of transport sweeps on orthogonal grids for any regular mapping of the grid cells to processors. Our model, which accounts for machine dependent parameters such a