A Parallelized Generalized Method of Cells Framework for Multiscale Studies of Composite Materials

Abstract

This paper presents a parallelized framework for a multi-scale material analysis method called the generalized method of cells (GMC) model which can be used to effectively homogenize or localize material properties over two different length scales. Parallelization is utlized at two instances: (a) for the solution of the governing linear equations, and (b) for the local analysis of each subcell. The governing linear equation is solved parallely using a parallel form of the Gaussian substitution method, and the subsequent local subcell analysis is performed parallely using a domain decomposition method wherein the lower length scale subcells are equally divided over available processors. The parellization algorithm takes advantage of a single program multiple data (SPMD) distributed memory architecture using the Message Passing Interface (MPI) standard, which permits scaling up of the analysis algorithm to any number of processors on a computing cluster. Results show significant decrease in solution time for the parallelized algorithm compared to serial algorithms, especially for denser microscale meshes. The consequent speed-up in processing time permits the analysis of complex length scale dependent phenomenon, nonlinear analysis, and uncertainty studies with multiscale effects which would otherwise be prohibitively expensive.