A parallel programming environment for adaptive p-version finite element analysis

Abstract

This paper presents a parallel programming environment for solving large-scale problems using adaptive p-version finite element approach. A scalable parallel feedback algorithm based on domain decomposition technique has been developed to incorporate the parallelism in adaptive finite element analysis of large-scale structures. This algorithm is implementable on MIMD type parallel processors, and uses p-extension of the finite element method. Modeling with p-version finite elements needs special considerations of load-balancing, and this has been incorporated in present domain decomposition technique using semi-empirical approach. The Connection Machine's CM-5 system has been used to implement the present system. Most of the previous attempts to parallelize adaptive finite element analysis were confirmed to parallel algorithms for direct or iterative equation solvers, and did not produce satisfactory performance because of small granularity of parallel tasks. Also these efforts were based on h-version of the finite element method, and hence could not exploit some of the special advantages available in p-vision of finite element approach. As the feedback algorithm is based on an iterative scheme, utilizing the domain decomposition technique, it produced good performance, particularly for large-scale structures. It has been tested for a number of regular and irregular two-dimensional problems showing good convergence characteristics.