A parallel finite element method with a supercomputer network

Abstract

Computer simulations are about to replace experiments in various fields, and the scale of the models to be simulated tend to be extremely large. To perform large-scale finite element analyses, the authors propose the parallel use of multiple supercomputers connected to one another through a highspeed network. In other words, a supercomputer network is regarded as a parallel computer. As a parallel numerical algorithm for the finite element analysis, we adopt the domain decomposition method (DDM) combined with an iterative solver, i.e. the conjugate gradient (CG) method, where a whole analysis domain is fictitiously divided into a number of subdomains without overlapping. Finite element analyses of the subdomains are performed under the constraint of both displacement continuity and force equivalence among subdomains. Such a constraint can be satisfied through iterative calculations such as the CG method. The present DDM-based parallel finite element algorithm is combined with the server-client model for data and processor management to have the workload balanced dynamically between the processors, and is implemented first on an engineering workstation (EWS) network and then on a supercomputer network. The accuracy and parallel performance of the present system are tested using the network composed of various EWSs. Finally, it is demonstrated that the present system implemented on the supercomputer network can solve the three-dimensional elasticity problem of over one million degrees of freedom at an extremely high average speed of 1.74 GFLOPS. § § This study has received the 1990 Cray Gigaflop Performance Award.