Finite Element Analysis in Concurrent Processing: Computational Issues

The purpose of this research is to investigate the potential application of new methods for solving large-scale static structural problems on concurrent computers. It is well known that traditional single-processor computational speed will be limited by inherent physical limits. The only path to achieve higher computational speeds lies through concurrent processing. Traditional factorization solution methods for sparse matrices are ill suited for concurrent processing because the null entries get filled, leading to high communication and memory requirements. The research reported herein investigates alternatives to factorization that promise a greater potential to achieve high concurrent computing efficiency. Two methods, and their variants, based on direct energy minimization are studied: a) minimization of the strain energy using the displacement method formulation; b) constrained minimization of the complementary strain energy using the force method formulation. Initial results indicated that in the context of the direct energy minimization the displacement formulation experienced convergence and accuracy difficulties while the force formulation showed promising potential.