In this paper, parallel library, portable extensible toolkit for scientific computation (PETSc), is used
to solve linear systems in soil-water coupled finite element method (FEM) for geotechnical problems. The parallel
environment is integrated into GLEAVES, which is a geotechnical software package used for the finite element
simulation. The linear system Ax = b which is a fundamental and the most time-consuming part of the FEM is
solved with iterative solvers in PETSc. In order to find a robust and effective combination of iterative solvers and
corresponding preconditioners for the soil-water coupled problems, performance evaluations on Krylov subspace
methods and four preconditioners are carried out. The results indicate that general minimal residual (GMRES)
method coupled with preconditioners can provide an effective solution. The application to a construction project
is presented to illustrate the potential of the proposed solution.
DI Dong-chao (狄东超), YE Guan-lin (叶冠林), XIA Xiao-he (夏小和), WANG Jian-hua* (王建华)
. Application of PETSc in Soil-Water Coupled Geotechnical Problems[J]. Journal of Shanghai Jiaotong University(Science), 2013
, 18(4)
: 401
-408
.
DOI: 10.1007/s12204-013-1409-y
[1] Chaudhary K B. Preconditioners for soil-structure interaction problems with significant material stiffness contrast [D]. Singapore: Department of Civil Engineering, National University of Singapore, 2010.
[2] Zhang You-liang, Feng Xia-ting, Ru Zhong-liang. Large-scale high performance parallel finite element system based on domain decomposition method in geomechanics [J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(21): 3636-3641 (in Chinese).
[3] Guo Y, Jin X, Ding J. Parallel numerical simulation with domain decomposition for seismic response analysis of shield tunnel [J]. Advances in Engineering Software, 2006, 37(7): 450-456.
[4] Chan S H, Phoon K K, Lee F H. A modified Jacobi preconditioner for solving ill-conditioned Biot’s consolidation equations using symmetric quasi-minimal residual method [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(10): 1001-1025.
[5] Phoon K K, Chan S H, Toh K C, et al. Fast iterative solution of large undrained soil-structure interaction problems [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, 27(3): 159-181.
[6] Balay S, Brown J, Buschelman K, et al. PETSc users manual [EB/OL]. (2011-09-08) [2012-09-10]. http://www.mcs.anl.gov/petsc.
[7] Sheng Jia-ren, Ye Guan-lin, Wang Jian-hua. Soilwater coupled numerical simulation on undergroundcavern excavation in soft rock grond [J]. Journal of Zhejiang University: Engineering Science, 2012, 46(5): 785-790 (in Chinese).
[8] Wang Wen-qing, Kolditz O. Sparse matrix and solver objects for parallel finite element simulation of multi-field problems [C]// Second International Conference on High performance computing and applications. Shanghai, China: HPCA, 2010: 418-425.
[9] Zhang Feng. Computational soil mechanics [M]. Beijing: China Communications Press, 2007: 142-161 (in Chinese).
[10] Manguoglu M, Sameh A H, Saied F, et al. Preconditioning techniques for nonsymmetric linear systems in the computation of incompressible flows [J]. Journal of Applied Mechanics, 2009, 76(2): 1-7.
[11] Saad Y, Schultz M H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems [J]. SIAM Journal on Scientific and Statistical Computing, 1986, 7(3): 856-869.
[12] Hestenes M R, Stiefel E. Methods of conjugate gradients for solving linear systems [J]. Journal of Research of the National Bureau of Standards, 1952, 49(6): 409-436.
[13] Sonneveld P. CGS, a fast lanczos-type solver for nonsymmetric linear systems [J]. SIAM Journal on Scientific and Statistical Computing, 1989, 10(1): 36-52.
