Feasibility Study and Predictability on the Performance of Parallel FEM Using Clusters on WAN

Abstract

With the rapid growth of WAN infrastructures and development of Grid middleware, the cluster-of-clusters has become a realistic methodology for executing computationdemanding applications. While distributed computing or loosely connected applications have been successfully ported to the Grid environment, few tightly connected applications such as parallel finite element analysis (FEA) have been attempted. In this paper we focus on an iterative solver which is often used in FEA: the conjugate gradient (CG) method. By using both predictions and numerical experiments we evaluate the performance of the CG method parallelized via domain decomposition. From numerical experiments we measure the inter-cluster execution time and find it to be close to that obtained by the slowest cluster. At the level of performance currently found in most WAN systems, as long as the number of processes is kept adequately small, the increase in communication cost due to WAN is small relative to the computation cost. For a very large test model which realistically requires the utilization of remote resources, the work ratio stays above 86% even for 64 processes. Especially for very large models, using the distributed environment is expected to be a practical methodology even for parallel computations with communication as frequent as the one found in FEA. To evaluate the feasibility of parallel FEA on the C-of-C, we have proposed methods for a priori finding the optimal number of processes.