Truncated Newton Methods for Nonlinear Finite Element Analysis

In the present study procedures for the solution of large-scale nonlinear algebraic discrete equations arising from the application of the finite element method to structural analysis problems are described and evaluated. The methods are based on Newton’s method for the outer iterations, while for the linearized problem in each iteration the preconditioned conjugate gradient (03) method is employed. This combination for the outer and inner iterations allows the use of less accuracy in computing exact Newton directions when far from the solution and the gradual increase in accuracy for the inner loops as the final solution is approached. This technique leads to the truncated Newton methods. Two preconditioning techniques for CG have been described and compared, namely the partial preconditioning and the partial elimination. Both techniques use a drop-off parameter J/ to control the computer storage demands for the extra matrix required. The results of two test examples are very encouraging as they show that the proposed method can be very effective in the solution of nonlinear finite element problems.