A Comparison of Element-By-Element Preconditioned Iterative Methods for Solid and Structural Mechanics

Abstract

Past work with element-by-element (EBE) preconditioned conjugate gradient iterative solution strategies has shown these techniques can be effective for large-scale, three-dimensional calculations in solid and structural mechanics. Significant gains over the profile storage direct solution method traditionally used in implicit finite element codes have been observed for a variety of real engineering analyses, especially in solid mechanics. Structural mechanics applications have proved less successful due to the ill-conditioned linear systems engendered by standard structural discretizations. This lack of robustness has recently motivated reconsideration of Lanczos-based algorithms as alternative iterative drivers. In this paper we compare the relative strengths of the conjugate gradient and Lanczos drivers when coupled with EBE preconditioning. The performance of the two methods is characterized, and compared with direct solution, using a model problem and a number of real engineering meshes. These examples suggest that the conjugate gradient method remains superior for large-scale computation.