Exact three-dimensional time-dependent wave packet calculations on the Connection Machine

Summary In this paper, we report our massively parallel implementation of grid techniques for the solution of the time-dependent Schrödinger equation in three spatial dimensions on the Connection Machine, which is a Single Instruction Multiple Data (SIMD) computer. Most of the operations involved in this calculation may be executed independently for each grid point. The few operations which cannot be executed independently are implemented using parallel communication algorithms. In addition, we report a simple modification of the multidimensional FFT, which provides an estimated 15% reduction in computational complexity relative to the standard 2-D FFT. It is suggested that this modification may be very well suited to hypercube communication topologies.