The iterative group implicit algorithm for parallel transient finite element analysis

The Iterative Group Implicit (IGI) algorithm is developed for the parallel solution of general structural dynamic problems. In this method the original structure is partitioned into a number of a subdomains. Each subdomain is solved independently and therefore concurrently, using any traditional direct solution method. The IGI algorithm is an extension of the Group Implicit (GI) algorithm, and similarly to that method compatibility of the interface degrees of freedom is restored using a mass averaging rule. However, unlike the GI algorithm, in the IGI algorithm an iterative procedure is devised to restore equilibrium at the interface degrees of freedom. The IGI method has the same algorithmic characteristics as the underlying solution method used to solve each subdomain. Furthermore, the solution obtained by this method, once the iteration converges, is the same as the one obtained if the subdomain solution method is used to solve the whole structure. Numerical studies are carried out which demonstrate that the performance of the IGI algorithm is superior to that of the GI algorithm both in terms of accuracy and e$ciency. Finally, the IGI method is highly modular and scalable, and therefore very well suited for distributed and parallel computing