Massively parallel high-energy time-dependent wave-packet calculations

Summary The exact solution of the time-dependent Schrödinger equation is obtained using a parallel implementation of the standard grid techniques. Most of the operations involved in this calculation may be executed concurrently for each of the grid points. For the few operations which may not be executed concurrently, we have implemented parallel algorithms. In our two-dimensional implementation on the Connection Machine, we have obtained optimal speed-up — that is, by usingN processors we achieve a speed-up which is proportional toN. In addition to the discussion of our 2-dimensional implementation, we shall discuss our proposed 3-dimensional implementation of these grid techniques.