Use of sparse iterative methods for the resolution of three‐dimensional soil/structure interaction problems

In this paper we present a study of the performance of sparse iterative solvers regarding the resolution of three-dimensional and non-linear problems encountered in soil/structure interaction. It is composed of two parts. In the first one, we present briefly iterative methods and preconditioners used in this study, then we analyse their performance on three soil/structure interaction problems: a shallow foundation under a vertical loading, a single pile subjected to a lateral loading and the construction of a lined tunnel in a soft soil. Tests are performed assuming an elastic–perfectly plastic constitutive law for the soil material with a non-associated Mohr–Coulomb flow rule. Copyright © 1999 John Wiley & Sons, Ltd.

[1]  Hussein Mroueh.  Tunnels en site urbain : modélisation numérique et intéraction creusement - ouvrages existants , 1998 .

[2]  U. M. Yang,et al.  A family of preconditioned iterative solvers for sparse linear systems , 1995 .

[3]  Claude Pommerell,et al.  Solution of large unsymmetric systems of linear equations , 1992 .

[4]  C. Lanczos.  Solution of Systems of Linear Equations by Minimized Iterations1 , 1952 .

[5]  O. Axelsson.  Iterative solution methods , 1995 .

[6]  Martin H. Gutknecht,et al.  Variants of BICGSTAB for Matrices with Complex Spectrum , 1993, SIAM J. Sci. Comput..

[7]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[8]  Tony F. Chan,et al.  A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems , 1994, SIAM J. Sci. Comput..

[9]  P. Sonneveld.  CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .

[10]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[11]  Manolis Papadrakakis.  Solving Large-scale Problems in Mechanics , 1993 .

[12]  U. Yang,et al.  A new family of preconditioned iterative solvers for nonsymmetric linear systems , 1995 .

[13]  C. Brezinski,et al.  Look-ahead in Bi-CGSTAB and other product methods for linear systems , 1995 .

[14]  Tony F. Chan,et al.  Composite Step Product Methods for Solving Nonsymmetric Linear Systems , 1996, SIAM J. Sci. Comput..

[15]  Claude Brezinski,et al.  Breakdowns in the implementation of the Lánczos method for solving linear systems , 1997 .

[16]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .