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| A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS | |
| Huang, JZ; Yang, C; Cai, XC | |
| 2016 | |
| Source | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| ISSN | 1064-8275 |
| Volume | 38Issue:3Pages:A1701-A1724 |
| English Abstract | Most existing methods for calculating the steady state solution of the lattice Boltzmann equations are based on pseudo time stepping, which often requires a large number of time steps especially for high Reynolds number problems. To calculate the steady state solution directly without the time integration, in this paper we propose and study a nonlinearly preconditioned inexact Newton algorithm with a domain decomposition based linear solver for parallelization. More precisely, the proposed algorithmic framework involves an implicit, second-order discretization, a two-level inexact Newton method, and a nonlinear elimination preconditioner to accelerate the convergence of Newton iteration. A nonstandard, pollution removing, coarse space is introduced for the two-level method. Numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm, especially for problems at a high Reynolds number. A comparison is also included to show the superiority of the proposed approach over other explicit and implicit methods in terms of the total compute time measured on a parallel computer.; Most existing methods for calculating the steady state solution of the lattice Boltzmann equations are based on pseudo time stepping, which often requires a large number of time steps especially for high Reynolds number problems. To calculate the steady state solution directly without the time integration, in this paper we propose and study a nonlinearly preconditioned inexact Newton algorithm with a domain decomposition based linear solver for parallelization. More precisely, the proposed algorithmic framework involves an implicit, second-order discretization, a two-level inexact Newton method, and a nonlinear elimination preconditioner to accelerate the convergence of Newton iteration. A nonstandard, pollution removing, coarse space is introduced for the two-level method. Numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm, especially for problems at a high Reynolds number. A comparison is also included to show the superiority of the proposed approach over other explicit and implicit methods in terms of the total compute time measured on a parallel computer. |
| Indexed Type | SCI |
| Keyword | Steady State Lattice Boltzmann Equations Inexact Newton Algorithm Nonlinear Preconditioning Pollution Removing Coarse Space Parallel Scalability |
| Department | Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China. Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China. Chinese Acad Sci, State Key Lab Comp Sci, Beijing 100190, Peoples R China. Univ Colorado, Dept Comp Sci, Boulder, CO 80309 USA. |
| Language | 英语 |
| WOS ID | WOS:000385282800019 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/17421 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Huang, JZ,Yang, C,Cai, XC. A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2016,38(3):A1701-A1724. |
| APA | Huang, JZ,Yang, C,&Cai, XC.(2016).A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,38(3),A1701-A1724. |
| MLA | Huang, JZ,et al."A NONLINEARLY PRECONDITIONED INEXACT NEWTON ALGORITHM FOR STEADY STATE LATTICE BOLTZMANN EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 38.3(2016):A1701-A1724. |
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