Time scaling in the parallel processing simulation of diffusion processes

A local interaction simulation approach, based on parallel processing, allows us to treat complex diffusion problems in very large lattices or complex media. In order to study the time evolution, e.g., of microscopic systems, we present here a time scaling method, which can reduce the number of time steps (and therefore the computer time) of several orders of magnitude, up to a manageable number (e.g., 104 or 105). Several examples under different assumptions demonstrate the applicability and reliability of the proposed method.