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A parallel boundary element formulation for determining effective properties of heterogeneous media
Author(s) -
Ingber Marc S.,
Womble David E.,
Mondy Lisa A.
Publication year - 1994
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.1620372209
Subject(s) - discretization , boundary element method , computer science , mimd , boundary (topology) , finite element method , representative elementary volume , computational science , parallel computing , mathematics , mathematical analysis , physics , thermodynamics
This paper presents a parallel implementation of the boundary element method for MIMD computer architectures to determine the effective properties of two heterogeneous physical systems. The first physical system is comprised of spheres sedimenting in a viscous fluid at low Reynolds numbers. The effective property is characterized by the hindered settling function which is a measure of the average sedimentation velocity. The second physical system is a short‐fibre reinforced composite. The effective property for this system is the composite modulus. The determination of effective properties of heterogeneous media requires performing statistical analyses of several realizations of physical systems based on defining characteristics of the media. The boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method. However, as the number of heterogeneities to be modeled is increased so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a parallel boundary element formulation based on the torus‐wrap mapping. In this approach, blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors. The torus‐wrap mapping can be shown to minimize communication volume between processors during the LU factorization. Therefore, the present formulation scales well with increases in the number of processors.