Water Science and Engineering 2011, 4(3) 317-328 DOI:   10.3882/j.issn.1674-2370.2011.03.008  ISSN: 1674-2370 CN: 32-1785/TV

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massive concrete
 symmetric successive over relaxation-preconditioned conjugate gradient method (SSOR-PCGM)
 improved iteration format
finite element method (FEM)
numerical simulation
NIE Zhi-Jiang
Article by Han,l
Article by Zhang,Z.M
Article by Nie,Z.J

Application of SSOR-PCG method with improved iteration format in FEM simulation of massive concrete

Lin HAN*, Zi-ming ZHANG, Zhi-qiang NI

College of Mechanics and Materials, Hohai University, Nanjing 210098, P. R. China


 In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method (SSOR-PCGM) with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete (RCC) gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.

Keywords massive concrete     symmetric successive over relaxation-preconditioned conjugate gradient method (SSOR-PCGM)     improved iteration format   finite element method (FEM)    numerical simulation  
Received 2010-10-15 Revised 2011-01-17 Online: 2011-09-30 
DOI: 10.3882/j.issn.1674-2370.2011.03.008

This work was supported by the National Natural Science Foundation of China (Grant No. 50808066).

Corresponding Authors: Lin HAN
Email: lion_han@hhu.edu.cn
About author:


Bai, Z. Z., and Wang, Z. Q. 2006. Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems. Journal of Computational and Applied Mathematics, 187(2), 202-226. [doi:10.1016/j.cam.2005.03.044]
Chen, R. S., Yung, E. K. N., Chan, C. H., and Fang, D. G. 2000. Application of the preconditioned conjugate- gradient algorithm to the edge FEM for electromagnetic boundary-value problems. Microwave and Optical Technology Letters, 27(4), 235-238. [doi:10.1002/1098-2760(20001120)27:4<235::AID-MOP5> 3.0.CO;2-8]
Chen, R. S., Tsang, K. F., and Mo, L. 2002a. Wavelet-based sparse approximate inverse preconditioned CG algorithm for fast analysis of microstrip circuits. Microwave and Optical Technology Letters, 35(5), 383-389. [doi:10.1002/mop.10615]
Chen, R. S., Yung, E. K. N., Chan, C. H., Wang, D. X., and Fang, D. G. 2002b. Application of the SSOR preconditioned CG algorithm to the vector FEM for 3D full-wave analysis of electromagnetic-field boundary-value problems. IEEE Transactions on Microwave Theory and Techniques, 50(4), 1165-1172. [doi:10.1109/22.993420]
Chen, R. S., Ping, X. W., Yung, E. K. N., Chan, C. H., Nie, Z., and Hu, J. 2006. Application of diagonally perturbed incomplete factorization preconditioned conjugate gradient algorithms for edge finite-element analysis of Helmholtz equations. IEEE Transactions on Antennas and Propagation, 54(5), 1604-1608. [doi:10.1109/TAP.2006.874358]
Chen, Y. L., and He, J. 1998. Simulation on temperature and thermal stress distribution of RCC gravity dam during construction by using 3D FEM floating mesh method. Journal of Hydraulic Engineering, 29(s1), 3-6. (in Chinese)
Dai, H. 2001. Krylov subspace methods for solving large scale matrix problems. Journal of Nanjing University of Aeronautics and Astronautics, 33(2), 139-145. (in Chinese)
Feng, Y. T., and Owen, D. R. J. 1996. Conjugate gradient methods for solving the smallest eigenpair of large symmetric eigenvalue problems. International Journal for Numerical Methods in Engineering, 39(13), 2209-2229. [doi:10.1002/(SICI)1097-0207(19960715)39:13<2209::AID-NME951>3.0.CO;2-R]
Jiang, S. L., Yang, L., Alsoliby, S., and Zhou, G. F. 2007. PCG solver and its computational complexity for implicit control-volume finite-element method of RTM mold filling simulation. Composites Science and Technology, 67(15-16), 3316-3322. [doi:10.1016/j.compscitech.2007.03.030]
Karátson, J. 2008. Superlinear PCG algorithms: symmetric part preconditioning and boundary conditions. Numerical Functional Analysis and Optimization, 29(5-6), 590-611. [doi:10.1080/01630560802099399]
Kim, S. Y., and Im, Y. T. 2003. Parallel processing of 3D rigid-viscoplastic finite element analysis using domain decomposition and modified block Jacobi preconditioning technique. Journal of Materials Processing Technology, 134(2), 254-264. [doi:10.1016/S0924-0136(02)01107-X]
Kress, G., Siau, M., and Ermanni, P. 2005. Iterative solution methods for damage progression analysis. Composite Structures, 69(1), 21-33. [doi:10.1016/j.compstruct.2004.04.043]
Lin, S. Z. 1997. Improved iterative format of symmetric successive over relaxation-preconditioned conjugated gradient method. Journal of Numerical Methods and Computer Applications, (4), 266-270. (in Chinese)
Lin, S. Z. 1998. Application of preconditioned conjugated gradient method to finite element equations and program design. Journal of Hohai University (Natural Sciences), 26(3), 112-115. (in Chinese)
Lin, S. Z., and Su, H. D. 2003. Fast algorithms for stress analysis simulating construction process of massive concrete structures and applications. Journal of Yangtze River Scientific Research Institute, 20(6), 19-22. (in Chinese)
Saint-Georges, P., Warzee, G., Beauwens, R., and Notay, Y. 1996. High-performance PCG solvers for FEM structural analysis. International Journal for Numerical Methods in Engineering, 39(8), 1313-1340. [doi:10.1002/(SICI)1097-0207(19960430)39:8<1313::AID-NME906>3.0.CO;2-J]
Wilson, E. L. 1968. Determination of Temperatures Within Mass Concrete Structures. Berkeley: Department of Civil Engineering, University of California.
Wu, Y., and Luna, R. 2001. Numerical implementation of temperature and creep in mass concrete. Finite Elements in Analysis and Design, 37(2), 97-106. [doi:10.1016/S0168-874X(00)00022-6]
Zhang, Z. M., Song, Z. T., and Huang, H. Y. 2002. New theory on adiabatic temperature rise and heat conduction equation of concrete. Journal of Hohai University (Natural Sciences), 30(3), 1-6. (in Chinese)
Zhao, D. S., Bo, Z. H., Li, G. Y., and Du, D. J. 1994. Visco-elasticity analysis for concrete arch dams by using dynamic emulation method. Journal of Hydraulic Engineering, 25(8), 18-26. (in Chinese)
Zhu, B. F. 1994. Mixed-layer method for analysis of stresses by simulating the construction process of multilayered high concrete structures. Journal of Hydroelectric Engineering, 13(3), 21-30. (in Chinese)
Zhu, B. F., and Xu, P. 1996. Zone-merged algorithm and zoned different-step-length algorithm in the concrete simulation calculation. Water Power, (1), 38-43. (in Chinese)
Zhu, B. F. 1999. Thermal Stresses and Temperature Control of Mass Concrete. Beijing: China Electric Power Press. (in Chinese)

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