A cellular automation methodology for solving the wave equation

We describe a parallel finite difference algorithm in the form of a cellular automaton for solving the full form of the wave equation. Since we do not use the far field approximation, this algorithm is particularly effective for solving near- and intermediate field problems. Problems are solved in the time domain and real time animated displays show the field evolution. The algorithm is perfectly matched to the architecture of “single instruction multiple data” (SIMD) parallel processors. On the CM-200, for example, it typically takes several minutes to compute wave fields and display them on a 512X512 grid. A good personal computer, however, is sufficient to develop many interesting classroom demonstrations of wave propagation phenomena.