Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/352081 |
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| _version_ | 1832567337037856768 |
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| author | Xi Chen Kok Kwang Phoon |
| author_facet | Xi Chen Kok Kwang Phoon |
| author_sort | Xi Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ce7b9afa7d594472bce1ab94e72a1597 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ce7b9afa7d594472bce1ab94e72a15972025-02-03T01:01:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/352081352081Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated PlasticityXi Chen0Kok Kwang Phoon1Department of Geotechnical Engineering, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, ChinaDepartment of Civil and Environmental Engineering, National University of Singapore, E1A-07-14, Blk E1A, 07-03, 1 Engineering Drive 2, 117576, SingaporeTwo 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.http://dx.doi.org/10.1155/2012/352081 |
| spellingShingle | Xi Chen Kok Kwang Phoon Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity Journal of Applied Mathematics |
| title | Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity |
| title_full | Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity |
| title_fullStr | Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity |
| title_full_unstemmed | Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity |
| title_short | Applications of Symmetric and Nonsymmetric MSSOR Preconditioners to Large-Scale Biot's Consolidation Problems with Nonassociated Plasticity |
| title_sort | applications of symmetric and nonsymmetric mssor preconditioners to large scale biot s consolidation problems with nonassociated plasticity |
| url | http://dx.doi.org/10.1155/2012/352081 |
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