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

Ashwin Rai, T. Skinner, A. Chattopadhyay
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引用次数: 1

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.
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复合材料多尺度研究的单元框架并行化广义方法
本文提出了一种多尺度材料分析方法的并行化框架,称为广义单元法(GMC)模型,该模型可用于有效地均匀化或局部化两个不同长度尺度上的材料特性。在两种情况下使用并行化:(a)用于控制线性方程的解,(b)用于每个子单元的局部分析。控制线性方程使用高斯替换法的并行形式并行求解,随后的局部子单元分析使用域分解方法并行执行,其中较低长度尺度的子单元在可用的处理器上均匀划分。并行化算法利用使用消息传递接口(MPI)标准的单程序多数据(SPMD)分布式内存体系结构,该体系结构允许将分析算法扩展到计算集群上的任意数量的处理器。结果表明,与串行算法相比,并行算法的求解时间显著减少,特别是对于更密集的微尺度网格。随之而来的处理时间的加快使得复杂长度尺度依赖现象的分析、非线性分析和多尺度效应的不确定性研究成为可能,否则这些研究将会非常昂贵。
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