A PARALLEL BOUNDARY-ELEMENT FORMULATION FOR DETERMINING EFFECTIVE PROPERTIES OF HETEROGENEOUS MEDIA

This paper presents a parallel implementation of the boundary element method for MIMD computer architectures to determine the effective prop erties of two heterogeneous physical systems. The first physical syste m is comprised of spheres sedimenting in a viscous fluid at low Reynol ds numbers. The effective property is characterized by the hindered se ttling function which is a measure of the average sedimentation veloci ty. The second physical system is a short-fibre reinforced composite. The effective property for this system is the composite modulus. The d etermination of effective properties of heterogeneous media requires p erforming statistical analyses of several realizations of physical sys tems based on defining characteristics of the media. The boundary elem ent method is particularly well suited for studying such systems becau se of the simplification in the discretization associated with the met hod. However, as the number of heterogeneities to be modeled is increa sed so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a paral lel boundary element formulation based on the torus-wrap mapping. In t his approach, blocks of the coefficient matrix associated with the dis cretized boundary element equations are assigned to processors as oppo sed to more traditional parallel boundary element implementations wher e rows or columns are assigned to processors. The torus-wrap mapping c an 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.