Solution algorithms for finite element structural analysis employing preconditioned conjugate gradient methods

Abstract

This paper summarizes the experience of the authors in the use of conjugate gradient algorithms in finite element structural analysis. There are treated both linear static and dynamic problems. The solver for systems of linear equations corresponding to the static problem, and the extraction of eigenvalues and the corresponding eigenvectors in the case of vibraton analysis of structures are based on conjugate gradient algorithms. These iterative methods were coupled with preconditioning using an approximate Choleski decomposition. The computer program modules are using sparse storage technics for matrix operations, and they were incorporated in a PC version of the SAP V Liege finite element analysis program. The analysis of several structures by these methods shows an improvement of performances versus direct methods. The precision of numerical solving increases, while the computer time and storage requirements are diminished. These solvers are very advantageous especially in the case of large structures.