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A parallel Monte‐Carlo finite‐element procedure for the analysis of multicomponent random media
Author(s) -
Cruz Manuel E.,
Patera Anthony T.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620380703
Subject(s) - monte carlo method , discretization , finite element method , domain decomposition methods , computer science , hypercube , homogenization (climate) , porous medium , mathematics , mathematical optimization , algorithm , statistical physics , parallel computing , mathematical analysis , physics , biodiversity , ecology , statistics , geotechnical engineering , biology , porosity , engineering , thermodynamics
Abstract 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.