Task Pool Teams Implementation of the Master Equation Approach for Random Sierpinski Carpets

We consider the use of task pool teams in implementation of the master equation on random Sierpinski carpets. Though the basic idea of dynamic storage of the probability density reported earlier applies straightforward to random carpets, the randomized construction breaks up most of the simplifications possible for regular carpets. In addition, parallel implementations show highly irregular communication patterns. We compare four implementations on three different BeowulfCluster architectures, mainly differing in throughput and latency of their interconnection networks. It appears that task pool teams provide a powerful programming paradigm for handling the irregular communication patterns that arise in our application and show a promising approach to efficiently handle the problems that appear with such randomized structures. This will allow for highly improved modelling of anomalous diffusion in porous media, taking the random structure of real materials into account.