The Solution of the Field Equations

An efficient method for the solution of the field equations is a necessary requirement for the practical implementation of the particle simulation algorithms that have been described. If we consider a typical computer experiment of 1,000 timesteps and an availability of one hour of computer time, it is clear that the solution of the field equations (which in a well-balanced calculation will be about half the cycle time) must not normally exceed a few seconds. For a machine with an average arithmetic-operation time of one microsecond, and a space mesh of about N_g = 10,000 points (say 20³ or 100²),* we require techniques that will obtain the solution in less than 100 arithmetic operations (or ~ 100 μs) per point. In fact the best available transform methods, where applicable, can achieve solution times of about 20 operations per point.