An embarrassingly parallel algorithm for random walk simulations on random fractal structures

Abstract

Anomalous diffusion is often simulated by random walks on random fractal structures. As existing simulation methods either lack a high degree of parallelism or impose restrictions on the choice of fractal structures, a new approach is proposed here.We present a parallel algorithm for simulating random walks on fractal structures that is suitable for a wide variety of hardware architectures. The degree of parallelism of the algorithm equals the number of random walkers, which is achieved by its communication-avoiding design. In contrast to other approaches, the random fractal structure is not pre-computed at whole. Instead, only the surrounding of each random walker is calculated by the parallel threads while the random walker moves around on the fractal structure.