A Coarse Grid Correction to Domain Decomposition Based Preconditioners for Meso-Scale Simulation of Concrete

Abstract:

Meso-scale simulation is one of the important ways to study dynamic behaviors of concrete materials, while most of the simulation time is used to solve the sparse linear systems. Because the discrete grid is three dimensional and is of large scale, iterations are the best solutions. But the convergence depends on the distribution of the eigenvalues of the coefficient matrix, to make the eigenvalues distributed more closely each other, it is required to adopt preconditioning techniques. In this paper, with the characteristics of the sparse linear systems considered, there provides a coarse grid correction algorithm, which is based on domain decomposition preconditioners and aggregation of sub-domains, with each aggregated into a single super-node. A linear system with small scale size is formed, which contains the global information and the solution is used to correct the solution components of the original auxiliary linear system. For incomplete factorization preconditioner parallelized with block Jacobi, classic additive Schwarz, and factors combination techniques, the experiments show that the presented algorithm can improve the convergence rate and the efficiency.

• Periodical: Applied Mechanics and Materials (Volumes 204-208)
• Pages: 4683-4687
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.204-208.4683
• Online since: October 2012
• Authors: Jian Ping Wu, Jun Qiang Song, Wei Min Zhang, Huai Fa Ma
• Keywords: Coarse Grid Correction, Domain Decomposition, Meso-Scale Simulation of Concrete, Parallel Computing, Sparse Linear Systems

References

[1] Ma Huaifa, Chen Houqun, Study on Dynamic Damage Mechanism of Full-graded Dam Concrete and its Meso-scale Mechanics Analysis, China WaterPower Press, Beijing, (2008).

[2] Wu Jian-ping, Zhao Jun, Song Jun-qiang, Li Xiao-mei, Impact of two factors on several domain decomposition based parallel incomplete factorizations for the meso-scale simulation of concrete, The Third International Conference on Information and Computing Science(ICIC2010), IEEE Press, Jun. 2010, pp.346-349.

DOI: 10.1109/icic.2010.146

[3] K. Nakajima, H. Okuda, Parallel Iterative Solvers with Localized ILU Preconditioning for Unstructured Grids on Workstation Clusters, International Journal of Computational Fluid Dynamics, Vol. 12, No. 3/4, 1999, pp.315-322.

DOI: 10.1080/10618569908940835

[4] J. Zhang, On preconditioning Schur complement and Schur complement preconditioning, Electronic Transactions on Numerical Analysis, No. 10, 2000, pp.115-130.

[5] R. Bru, F. Pedroche, D. B. Szyld, Overlapping Additive and Multiplicative Schwarz Iterations for H-matrices, Linear Algebra and its Applications, No. 393, 2004, p.91–105.

DOI: 10.1016/j.laa.2003.10.022

[6] R. E. White, Multisplitting with different weighting schemes, SIAM J. Matrix Anal. Appl., Vol. 10, No. 4, 1989, pp.481-493.

DOI: 10.1137/0610034

[7] X. -C. Cai, M. Sarkis, A restricted additive Schwarz preconditioner for general sparse linear systems, SIAM J. Sci. Comput., No. 21, 1999, pp.792-797.

DOI: 10.1137/s106482759732678x

[8] Wu Jianping, Song Junqiang, Zhang Wei-min, Li Xiaomei, A Parallelization Method to Incomplete Factorization Preconditioning of Block Tridiagonal Linear Systems Based on 2-D Domain Decomposition, Chinese J. Computational Physics, Vol. 26, No. 1, 2009, pp.149-155.

[9] Wu Jianping, Wang Zhenghua, Li Xiaomei, Problems and Improvements to the Incomplete Cholesky Decomposition with Thresholds, Journal on Numerical Methods and Computer Applications, Vol. 24, No. 3, 2003, pp.207-214.