Parallel algorithms for the direct solution of finite element equations on a distributed memory computer

Abstract

This work constitutes the first phase of a long-term project, namely the efficient implementation of direct solution methods for complex finite element problems on distributed memory parallel computers. Although for the most part limited to the one-dimensional case, our results demonstrate the potential of parallel computing for this class of problems. It is found that the efficiency of the proposed algorithms increases as the problem size increases. We have shown that a performance model can be developed and used for predicting with good accuracy the behavior of the proposed algorithms. Finally, our preliminary results for the two-dimensional case are encouraging. Work is underway to further generalize the present approach to complex multi-dimensional problems.