A parallel Monte‐Carlo finite‐element procedure for the analysis of multicomponent random media

We present a new first‐principle framework for the prediction of effective properties and statistical correlation lengths for multicomponent random media. The methodology is based upon a variational hierarchical decomposition procedure which recasts the original multiscale problem as a sequence of three scale‐decoupled subproblems. The focus of the current paper is the computationally intensive mesoscale subproblem, which comprises: Monte‐Carlo acceptance–rejection sampling; domain generation and parallel partition based on Voronoi tesselation; parallel Delaunay mesh generation; homogenization‐theory formulation of the governing equations; finite‐element discretization; parallel iterative solution procedures; and implementation on message‐passing multicomputers, here the Intel iPSC/860 hypercube. Two (two‐dimensional) problems of practical importance are addressed: heat conduction in random fibrous composites, and creeping flow through random fibrous porous media.