Multigrid approaches to non‐linear diffusion problems on unstructured meshes
Multigrid approaches to non‐linear diffusion problems on unstructured meshes
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DOI：
10.1002/nla.262
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发表时间：
2001-12
影响因子：
4.3
通讯作者：
D. Mavriplis
中科院分区：
文献类型：
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作者：
D. Mavriplis
研究了三种多重网格法求解二维非结构化网格上高度非线性扩散问题的效率。这三种多重网格方法的区别主要在于处理控制方程非线性的方式。这些方法包括用于直接求解非线性方程的非线性全近似存储（FAS）多重网格方法，用于求解由非线性系统的牛顿线性化产生的线性系统的线性多重网格方法，以及基于非线性FAS多重网格方案的混合方案，但在每个级别上使用线性解算器作为平滑器。结果表明，在渐近收敛区域，所有方法在收敛给定数目的多网格循环中的非线性残差方面都是同样有效的，但由于线性求解器比非线性网格扫描的成本更低，因此在cpu时间上更有效。版权所有©2001约翰威利父子有限公司
The efficiency of three multigrid methods for solving highly non‐linear diffusion problems on two‐dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the non‐linearities of the governing equations are handled. These comprise a non‐linear full approximation storage (FAS) multigrid method which is used to solve the non‐linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non‐linear system, and a hybrid scheme which is based on a non‐linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that, in the asymptotic convergence region, all methods are equally effective at converging the non‐linear residual in a given number of multigrid cycles, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non‐linear grid sweeps. Copyright © 2001 John Wiley & Sons, Ltd.