The author discusses three performance issues that arose in an implementation of a time-driven battlefield simulation on a medium-scale multiprocessor. The problems are generic, so that the observations and conclusions are applicable to the general class of physical-domain simulations that use time-stepping to advance the simulation. The first issue is that of mapping the simulation onto the multiprocessor. Under the message-passing paradigm, the assignment of workload to processors has the single-most-important influence on performance. The second issue is that of performing redundant computation in order to avoid a certain amount of communication. This issue is important when the cost of communication is high. The third issue is the possibility of deadlock due to distributed contention for message buffers. A solution is outlined that ensures that deadlock does not occur.