Concurrent iterative solution of large finite element systems

A general iterative algorithm for the solution of large finite element systems of arbitrary domain geometry is designed to operate efficiently on modern computers with concurrent processors. The domain is recursively and automatically subdivided into the same number of subdomains as available processors. Convergence is ensured because of the Gauss–Seidel type of iterations operated on each subdomain and corresponding interface. This subdomain iterative solution approach is compatible with the other phases of a complete concurrent finite element analysis (concurrent stiffness formation and assembly and concurrent element post‐processing), from both the data structure and computation points of view. Implementation of the resulting stratagem on MIMD computers is presented. Several examples are run on a hypercube multiprocessor to validate the proposed algorithm and assess its performance. An efficiency of 91 per cent is achieved for a problem with 16,000 degrees‐of‐freedom.