Using the conjugate gradient method with preconditioning for solving FEM approximations of elasticity problems

Abstract

A fast assembly scheme for FEM sparse matrices is given. For the solution we compare the conjugate gradient and two preconditionings for this method in the case of plane strain elasticity and orthotropic materials with very stiff coefficients. The influence of fibre orientation on the number of iterations is tested. It is suggested to use the simple incomplete Crout scheme even when the resulting preconditioning matrix is not positive definite.

Citation

Bercovier, M. and Rosenthal, A. (1986), "Using the conjugate gradient method with preconditioning for solving FEM approximations of elasticity problems", Engineering Computations, Vol. 3 No. 1, pp. 77-80. https://doi.org/10.1108/eb023644