Space-time geometric multigrid method for nonlinear advection–diffusion problems
Space-time geometric multigrid method for nonlinear advection–diffusion problems
复制标题
非线性平流扩散问题的时空几何多重网格法
DOI：
10.1080/00036811.2022.2039387
复制
发表时间：
2022
影响因子：
1.1
通讯作者：
Wheeler, Mary F.
中科院分区：
文献类型：
--
作者：
Li, Hanyu;Wheeler, Mary F.
代数或几何多重网格法在延拓后通常会产生高频残差。本文发展了一种稳定的方法来消除几何多重网格方法中的高频残差，用于求解退化系数的非线性对流扩散问题。在这里，一个局部的问题是处理优化的子域网格细化。该方法采用牛顿法，当子域中的残差降到给定值（通常为非高频域中残差的平均值）时，迭代完成。采用过采样技术，通过在系数具有高对比度和复杂结构的区域中提供确定的流路来进一步提高稳定性。在继续全局牛顿迭代之前去除高频残差改善了全局收敛行为。
Multigrid methods, algebraic or geometric, commonly suffer from high frequency residuals after prolongation. This paper develops a stable approach to remove high frequency residuals for geometric multigrid methods for solving nonlinear advection–diffusion problems with degenerate coefficients. Here, a local problem is treated by optimization on subdomains with mesh refinements. Newton's method is utilized in the procedure and the iteration is completed when the residual in the subdomain is reduced to the given magnitude, usually set to be the average of residuals in the non-high-frequency domains. An oversampling technique is employed to further improve the stability by providing a definite flow path in regions where coefficients have high contrast and complex structures. Removing high frequency residuals before continuing the global Newton iteration improves global convergence behavior.
针对非线性两相流问题具有独立时间和空间适应性的顺序局部网格细化求解器
影响因子：
4.1
作者：
Li, Hanyu;Leung, Wing Tat;Wheeler, Mary F.
通讯作者：
Wheeler, Mary F.