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刘笑1, 徐小文2
刘笑, 徐小文. 求解多尺度稀疏矩阵的代数界面优先AMG光滑子[J]. 数值计算与计算机应用, 2023, 44(1): 1-11.
Liu Xiao, Xu Xiaowen. AN AMG SMOOTHER BASED ON ALGEBRAIC INTERFACE-PRIOR FOR SOLVING MULTL-SCALE SPARSE MATRICES[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 1-11.
Liu Xiao1, Xu Xiaowen2
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[1] Ruge J W, Stüben K. Algebraic multigrid[C]. In Multigrid methods, SIAM, 1987, 73-130. [2] 徐小文. 可扩展并行代数多重网格算法研究[D]. PhD thesis, 博士论文, 北京:中国工程物理研究院研究生部, 2007. [3] 徐小文, 莫则尧, 刘旭. 基于局部松驰和粗化策略的代数多重网格方法[J]. 数值计算与计算机应用,2009, (2):81-91. [4] Sterck H D, Yang U M, Heys J J. Reducing complexity in parallel algebraic multigrid preconditioners[J]. SIAM Journal on Matrix Analysis and Applications, 2006, 27(4):1019-1039. [5] Oliveira S, Deng Y. Preconditioned Krylov subspace methods for transport equations[J]. Progress in Nuclear Energy, 1998, 33(1-2):155-174. [6] Erlangga Y A, Nabben R. Algebraic multilevel Krylov methods[J]. SIAM Journal on Scientific Computing, 2009, 31(5):3417-3437. [7] Elman H, Howle V E, Shadid J, Shuttleworth R, Tuminaro R. A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations[J]. Journal of Computational Physics, 2008, 227(3):1790-1808. [8] Brandt A. General highly accurate algebraic coarsening[J]. Electronic Transactions on Numerical Analysis, 2000, 10(1):21. [9] der Vorst H A V. Bi-CGSTAB:A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems[J]. SIAM Journal on scientific and Statistical Computing, 1992, 13(2):631-644. [10] Saad Y. Iterative methods for sparse linear systems[M]. SIAM, 2003. [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] Kettler R. Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods[G]. In Multigrid methods, Springer, 1982, 502-534. [13] Brannick J J, Falgout R D. Compatible relaxation and coarsening in algebraic multigrid[J]. SIAM Journal on Scientific Computing, 2010, 32(3):1393-1416. [14] Mo Z, Xu X. Relaxed RS0 or CLJP coarsening strategy for parallel AMG[J]. Parallel Computing, 2007, 33(3):174-185. [15] Sterck H D, Yang U M. Coarsening and interpolation in algebraic multigrid:a balancing act[C]. In Presentation at the 9th Copper Mountain Conference on Multigrid Methods, 2004. [16] Livne O E. Coarsening by compatible relaxation[J]. Numerical linear algebra with applications, 2004, 11(2-3):205-227. [17] Ron D, Safro I, Brandt A. Relaxation-based coarsening and multiscale graph organization[J]. Multiscale Modeling & Simulation, 2011, 9(1):407-423. [18] Grauschopf T, Griebel M, Regler H. Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs[J]. Applied Numerical Mathematics, 1997, 23(1):63-95. [19] Brannick J, Brezina M, MacLachlan S, Manteuffel T, McCormick S, Ruge J. An energy-based AMG coarsening strategy[J]. Numerical linear algebra with applications, 2006, 13(2-3):133-148. [20] Wittum G. On the robustness of ILU smoothing[J]. SIAM journal on scientific and statistical computing, 1989, 10(4):699-717. [21] Thomas S, Carr A, Świrydowicz K, Day M. ILUT Smoothers for Hybrid C-AMG with Scaled Triangular Factors[J]. arXiv preprint arXiv:2111.09512, 2021. [22] Tang W P, Wan W L. Sparse approximate inverse smoother for multigrid[J]. SIAM Journal on Matrix Analysis and Applications, 2000, 21(4):1236-1252. [23] Luo P, Rodrigo C, Gaspar F J, Oosterlee C. On an Uzawa smoother in multigrid for poroelasticity equations[J]. Numerical Linear Algebra with Applications, 2017, 24(1):e2074. [24] Oosterlee C W. A GMRES-based plane smoother in multigrid to solve 3D anisotropic fluid flow problems[J]. Journal of Computational Physics, 1997, 130(1):41-53. [25] Swanson R, Turkel E, Yaniv S. Analysis of a RK/implicit smoother for multigrid[G]. In Computational Fluid Dynamics 2010, pages 409-417. Springer, 2011. [26] Evans D J, Yousif W. The Explicit Block Relaxation method as a grid smoother in the Multigrid V-cycle scheme[J]. International journal of computer mathematics, 1990, 34(1-2):71-78. [27] Kashi A, Vangara S, Nadarajah S, Castonguay P. Asynchronous fine-grain parallel implicit smoother in multigrid solvers for compressible flow[J]. Computers & Fluids, 2020, 198:104255. [28] Zeeuw P D. Incomplete line LU as smoother and as preconditioner[G]. In Incomplete Decomposition (ILU)-Algorithms, Theory, and Applications, Springer, 1993, 215-224. [29] Ghysels P, K losiewicz P, Vanroose W. Improving the arithmetic intensity of multigrid with the help of polynomial smoothers[J]. Numerical Linear Algebra with Applications, 2012, 19(2):253-267. [30] Kawai M, Iwashita T, Nakashima H, Marques O. Parallel smoother based on block red-black ordering for multigrid poisson solver[C]. In International Conference on High Performance Computing for Computational Science, pages 292-299. Springer, 2012. [31] Yang U M. Parallel algebraic multigrid methods-high performance preconditioners[G]. In Numerical solution of partial differential equations on parallel computers, pages 209-236. Springer, 2006. [32] Falgout R D, Vassilevski P S, Zikatanov L T. On two-grid convergence estimates[J]. Numerical linear algebra with applcations, 2005, 12(5-6):471-494. [33] Bank R E, Douglas C C. Sharp estimates for multigrid rates of convergence with general smoothing and acceleration[J]. SIAM journal on numerical analysis, 1985, 22(4):617-633. [34] Baker A H, Falgout R D, Kolev T V, Yang U M. Multigrid smoothers for ultraparallel computing[J]. SIAM Journal on Scientific Computing, 2011, 33(5):2864-2887. [35] Yang U M. On the use of relaxation parameters in hybrid smoothers[J]. Numerical Linear Algebra with Applications, 2004, 11(2-3):155-172. [36] Adams M, Brezina M, Hu J, Tuminaro R. Parallel multigrid smoothing:polynomial versus Gauss-Seidel[J]. Journal of Computational Physics, 2003, 188(2):593-610. [37] Bröker O, Grote M J, Mayer C, Reusken A. Robust parallel smoothing for multigrid via sparse approximate inverses[J]. SIAM Journal on Scientific Computing, 2001, 23(4):1396-1417. [38] Falgout R, Cleary A, Jones J, Chow E, Henson V, Baldwin C, Brown P, Vassilevski P, Yang U. Hypre User's Manual, Version 2.7[J]. Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory, Livermore, CA, 2010. [39] Xu X, Yue X, Mao R, Deng Y, Huang S, et al, JXPAMG:A Parallel Algebraic Multigrid Solver for Extreme-scale Numerical Simulations[C]. CCF Trans. HPC, 2022. https://doi.org/10.1007/s42514-022-00125-9 [40] Aage N, Andreassen E, Lazarov B S. Topology optimization using PETSc:An easy-to-use, fully parallel, open source topology optimization framework[J]. Structural and Multidisciplinary Optimization, 2015, 51(3):565-572. [41] Xu X, Mo Z. Algebraic interface-based coarsening AMG preconditioner for multi-scale sparse matrices with applications to radiation hydrodynamics computation[J]. Numerical Linear Algebra with Applications, 2017, 24(2):e2078. [42] https://www.solver-conference.cn/solverchallenge21/ [43] 裴文兵, 朱少平. 激光聚变中的科学计算[J]. 物理, 2009, 38(08):559-568. [44] 徐小文. 并行代数多重网格算法:大规模计算应用现状与挑战[J]. 数值计算与计算机应用,2019, 40(4):243-260. |
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