Engineering with Computers 2, 157-165 (1987) 9 Springer-Verlag New York Inc. 1987 Solution of Finite Element Systems on Concurrent Processing Computers Charbei Farhat, Edward Wilson, and Graham Powell Division of Structural Engineering and Structural Mechanics, University of California at Berkeley, Berkeley, California 94720 Abstract. A new computer program architecture for the solution of finite element systems using concurrent processing is pre- sented. The basic approach involves the automatic creation of substructures. A host provides control over a set of processors, each of which is assigned initially to one substructure, then dy- namically reassigned to the common interface for the solution of the complete system of substructures. Algorithm details are pre- sented fo each phase of the analysis. Results of analysis of large plate bending problems on a hypercube multicomputer are reported. For a system with 2,000 equations, an efficiency of 80 percent of the maximum theoreti- cal value was obtained using 16 processors. 1 Introduction At the present time, finite element systems are solved on a broad range of computer hardware from inexpensive microcomputers [1], to very expensive supercomputers [2,3]. The major limitation in the use of microcomputers for the solution of large sys- tems is that they may require large execution times. The current microcomputer hardware technology will increase in speed; however, we can only expect approximately a factor of 10 increase in speed during the next several years for this type of low-cost hard- ware. The cost of the central processing unit (CPU) and random access memory (RAM) within a micro- computer represents only a small fraction of the cost of the complete system. Therefore, it is possi- ble to increase the number of CPUs and RAM within a computer system at a small cost increase for each processor. The idea for using multiple processors for the solution of finite element systems was suggested Reprint requests: E. Wilson, Division of Structural Engi- neering and Structural Mechanics, University of California at Berkeley, Berkeley, CA 94720 over 10 years ago [4]. A special purpose multicom- puter known as the finite element machine was built and experimented at the NASA Langley Research Center [5]. However, commercial computers with multiple processors have been available only within the past few years. The engineering research com- munity is currently working on new or modified nu- merical algorithms in order to exploit the speed of these new computer systems [6-9]. The purpose of this paper is to present a new architecture for a finite element program that is designed to operate on any MIMD (multiple instruction multiple data streams) machine. Also, the same techniques can be used for nonstructural finite element problems. 2 Architecture of a Concurrent Processing Program In structural analysis the technique of dividing a large system into a system of substructures is very old and is still used extensively. For large aerospace structures, its use is often motivated by the fact that different components are designed concurrently by different groups or companies. Therefore, only the basic static and dynamic properties of the substruc- ture need to be communicated between groups. This approach has also resulted in computational saving. If the design of one component is changed, only that substructure needs to be reanalyzed and the global system of substructures resolved. In the case of limited nonlinear systems, only the sub- structures that are nonlinear need be studied incre- mentally with time. It is clear that this traditional substructuring ap- proach can be used with concurrent processors if the complete finite element system is subdivided so that each group of elements within a small domain is