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Journal of Applied Mathematics
Volume 2012, Article ID 352081, 15 pages
Research Article

Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity

1Department of Geotechnical Engineering, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
2Department of Civil and Environmental Engineering, National University of Singapore, E1A-07-14, Blk E1A, 07-03, 1 Engineering Drive 2, Singapore 117576

Received 12 October 2011; Revised 14 December 2011; Accepted 15 December 2011

Academic Editor: Massimiliano Ferronato

Copyright © 2012 Xi Chen and Kok Kwang Phoon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two solution schemes are proposed and compared for large 3D soil consolidation problems with nonassociated plasticity. One solution scheme results in the nonsymmetric linear equations due to the Newton iteration, while the other leads to the symmetric linear systems due to the symmetrized stiffness strategies. To solve the resulting linear systems, the QMR and SQMR solver are employed in conjunction with nonsymmetric and symmetric MSSOR preconditioner, respectively. A simple footing example and a pile-group example are used to assess the performance of the two solution schemes. Numerical results disclose that compared to the Newton iterative scheme, the symmetric stiffness schemes combined with adequate acceleration strategy may lead to a significant reduction in total computer runtime as well as in memory requirement, indicating that the accelerated symmetric stiffness method has considerable potential to be exploited to solve very large problems.