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PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Truncated Newton Methods for Nonlinear Finite Element Analysis
M. Papadrakakis and G.J. Gantes
Institute of Structural Analysis and Aseismic Research, National Technical University. Athens, Greece
M. Papadrakakis, G.J. Gantes, "Truncated Newton Methods for Nonlinear Finite Element Analysis", in B.H.V. Topping, (Editor), "Proceedings of the Third International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Edinburgh, UK, pp 159-167, 1987. doi:10.4203/ccp.4.18.2
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 (CG) method is employed.
This combination for the outer and inner iterations permits us not to spend much effort in computing exact Newton directions when far from the solution and gradually to increase the 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 psi to control the computer storage demands for the extra matrix required.
The results of two test examples are very encouraging by showing that the proposed method can be very effective in the solution of nonlinear finite element problems.
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