Parallelism in adaptivep-version finite element analysis

The object of the present research effort is to address the issues involved in the adaptive finite element solution of large-scale systems taking advantage of the recent developments in multiprocessor technology, and to implement adaptive p-version finite element methodologies on a suitable parallel computing system. A scalable parallel feedback algorithm for adaptive finite element modeling of large scale structures is presented. This algorithm is implementable on MIMD parallel processors, and uses the p-extension of the finite element method. The problem domain is decomposed into a number of suitable subdomains by using an automatic domain decomposer, and each subdomain is thereupon assigned to a processor in the multiprocessor system. Different objectives of the domain decomposition technique, including the special considerations while modeling with p-version finite elements, are described. An automatic static domain decomposition algorithm incorporating these objectives are implemented in C language. The Connection Machine's CM-5 system has been used to implement the present system. Most of the previous efforts to parallelize finite element analysis were confined to parallel algorithms for direct or iterative equation solvers, and did not produce satisfactory performance because of the small granularity of parallel tasks. Also, these efforts were based on the h-extension of the finite element method, and hence could not exploit some of the inherent advantages available in the p-extension. As the current algorithm utilizes the domain decomposition technique and is based on the p-version of the finite element method, it produced improved performance. The feedback algorithm is based on an iterative scheme derived from the domain decomposition technique for applications to problems of solid mechanics. The proposed parallel scheme was tested for a number of two-dimensional problems exhibiting desired performance.