An optimized parallel preconditioner for solving the coarse mesh finite difference equation

被引：0
作者：
Liu L. [1 ]
Zhu K. [1 ]
Hao C. [2 ]
Li F. [1 ]
机构：
[1] Institution of Nuclear and New Energy Technology, Tsinghua University, Beijing
[2] College of Nuclear Science and Technology, Harbin Engineering University, Harbin
来源：
Harbin Gongcheng Daxue Xuebao/Journal of Harbin Engineering University | 2021年 / 42卷 / 12期
关键词：
Coarse mesh finite difference; Generalized minimum residual method; Hybrid preconditioner; Incomplete LU decomposition; Modified incomplete LU decomposition; Parallel computing; Preconditioning; Reduced symmetric over-relaxation;
D O I：
10.11990/jheu.202107046
中图分类号：
学科分类号：
摘要：
The generalized minimal residual algorithm (GMRES) has been widely used to solve coarse mesh finite difference (CMFD) linear systems. However, the computational efficiency of GMRES depends on the preconditioning methods. The hybrid reduced symmetric successive over-relaxation and incomplete lower upper (ILU) preconditioner (RSILU) is an efficient preconditioning method. To further improve the preconditioning efficiency of the RSILU, two methods, namely, "modified ILU decomposition" and "approximate inversion of a diagonal block matrix" are used to optimize the RSILU. The numerical results show that the optimized RSILU preconditioning efficiency is further improved in the serial and parallel calculations. Moreover, the preconditioning time of the RSILU method for multigroup CMFD with a complex group structure is reduced by half. Finally, the VERA Problem #4 benchmark is used to comprehensively test the preconditioning efficiency of the optimized RSILU, and the overall calculation time of GMRES is reduced by 30% compared with that before optimization. Overall, the optimized RSILU addresses some of the shortcomings in previous methods and further improves the computational efficiency of the preconditioned parallel GMRES method in solving large-scale CMFD linear systems. Copyright ©2021 Journal of Harbin Engineering University.
引用
收藏
页码：1805 / 1812
页数：7
相关论文
共 12 条
  • [1] SMITH K S., Spatial homogenization methods for light water reactor analysis, (1980)
  • [2] SAAD Y., Iterative methods for sparse linear systems, (1996)
  • [3] BENZI M., Preconditioning techniques for large linear systems: a survey, Journal of computational physics, 182, 2, pp. 418-477, (2002)
  • [4] LI Ruipeng, SAAD Y., GPU-accelerated preconditioned iterative linear solvers, The journal of supercomputing, 63, 2, pp. 443-466, (2013)
  • [5] DOWNAR T, COLLINS B S, GEHIN J C, Et al., MPACT Theory Manual, Version 2.2.0, (2016)
  • [6] XU Yunlin, HAO Chen, A novel and efficient hybrid RSILU preconditioner for the parallel GMRES solution of the coarse mesh finite difference equations for practical reactor simulations, Nuclear science and engineering, 194, 2, pp. 104-119, (2020)
  • [7] ZHANG Wusheng, XUE Wei, LI Jianjiang, Et al., MPI parallel programming tutorial, (2009)
  • [8] GU Tongxiang, AN Hengbin, LIU Xingping, Et al., Iterative methods and precondition techniques, (2015)
  • [9] HAO Chen, XU Yunlin, DOWNAR T J., Multi-level coarse mesh finite difference acceleration with local two-node nodal expansion method, Annals of nuclear energy, 116, pp. 105-113, (2018)
  • [10] SMITH M A, LEWIS E E, NA B C., Benchmark on deterministic 3-D MOX fuel assembly transport calculations without spatial homogenization, Progress in nuclear energy, 48, 5, pp. 383-393, (2006)
12