Stochastic modelling of diffusion equations on a parallel machine

Abstract

We present the parallelization of the code “MIXAGE” 3D on the T-Node tandem of JRC-Ispra. This code solves numerically parabolic systems of partial differentiation equations. These equations, which govern many physical, chemical or biological phenomena, describe time-dependent diffusion in heterogeneous media. We mainly use stochastic differential equations associated to the equation ∂f/ ∂t=▿( D▿ f). Moreover, we define the evolution operators corresponding to the different physical phenomena. By a process that we call “mixing”, we construct the general solution considering simultaneously all the physical phenomena. In view of the implementation of the code “MIXAGE” 3D on the T-Node, we have chosen geometric parallelization. Using a matrix 7 × 7 processor, the CPU time reached with the T-Node is of the same order as with the CRAY II machine.