Abstract
Element-by-element iterative solution methods have been shown to be effective for solving large, sparse linear systems of equations with a positive definite stiffness matrix. In this paper the iterative method GMRES will be described. This solution method is also suited for solving nonsymmetric systems of equations. As acceleration technique an element-by-element preconditioner has been employed. Attention is focused mainly on the convergence behaviour of the method. The calculations described in this paper have been performed with the finite element package DIANA.
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References
Amoldi, W.E. ‘The principle of minimized iteration in the solution of the matrix eigenvalue problem.’, Quart. Appl. Math. 9, pp. 17–29 (1951)
de Borst, R., Kusters, G.M.A., Nauta, P. and de Witte, F.C. ‘DIANA- a comprehensive, but flexible finite element system.’ In Finite Element Systems: A Handbook (Edited by C.A. Brebbia). Springer, Berlin (1985)
Feenstra, P.H. ‘Numerical Simulation and Stability Analysis of Crack Dilatancy Models.’, TNOIBBC report nr. BI–89–191, TU–Delft report 25.2–89–2–19, Delft, Netherlands (1989)
Crisfield, M.A. ‘Finite elements and solution procedures for structural analysis.’ Swansea U.K. (1986)
Hughes, J.R., Levit, I. en Winget, J. ‘An clement by element solution algorithm for problems of structural and solid mechanics.’ J. Comp. meth. appl. mech. Engng. 36 pp. 241–254 (1983)
Johnson, C. ‘Numerical solution of differential equations by the finite element method, Cambridge University Press (1987)
Nour-Omid B. en Parlett, B. N. ‘Elementpreconditioning using splitting techniques.’ SIAM J. of Computational Physics 44, pp. 131–155 (1981)
Reinhardt, H.N. en Walraven J.L. ‘Theory and experiments on the mechanical behaviour of cracks in plain and reinforced concrete subjected to shear loading.’, HERON, vol. 26 no la (1981)
Saad, Y. en Schultz, M.H. ‘GMRES: A Generalized Minimal Residual Algorithm for Solving Non-symmetric Linear Systems.’, SIAM J. Sci. Stat. Comput. Vol 7 No 3, pp. 856–869 (1986)
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© 1990 Kluwer Academic Publishers
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van Gijzen, M.B., Nauta, P. (1990). An element-by-element solution algorithm for nonsymmetric linear systems of equations. In: Dijksman, J.F., Nieuwstadt, F.T.M. (eds) Integration of Theory and Applications in Applied Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2125-2_21
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DOI: https://doi.org/10.1007/978-94-009-2125-2_21
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