A HIGHLY EFFICIENT ITERATIVE PARALLEL COMPUTATIONAL METHOD FOR FINITE ELEMENT SYSTEMS

A fully parallel algorithm for the solution of a finite element system using a MIMD (multiple‐instruction multiple‐data architecture) parallel computer is presented. The formulation includes a simple domain decomposer that automatically divides a finite element mesh into a list of subdomains to guarantee the load balancing. Furthermore, each subdomain is assigned to a processor of a parallel computer and treated as a sub‐finite element system with information exchanged through the interface between two adjacent subdomains. With this new algorithm, these sub‐finite element systems are solved fully parallelly as independent finite element systems, not only the computations of the interior nodes but also the computations of the interface nodes can be executed parallelly. Also, the inherently sequential Gauss‐Seidel and SOR schemes are altered into fully parallel iterative schemes. An implementation of this new scheme on an iPSC/2 D5 Hypercube Concurrent Computer reached an efficiency of more than 100% when compared with the sequential SOR scheme.