In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which combines a piecewise constant interpolation and the restriction operator by Wesseling/Khalil with a line-wise relaxation procedure. A local Fourier analysis is performed for the case of a Cartesian uniform grid. The method shows a robust convergence for different full tensor coefficient problems and several rough quadrilateral grids.

中文翻译：

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四边形粗糙网格上达西问题的多点通量近似的多网格求解器

在这项工作中，提出了一种有效的黑盒型多重网格方法，用于解决逻辑矩形网格上的达西问题的多点通量近似。该方法基于以单元为中心的多重网格算法，该算法将分段常量插值和Wesseling / Khalil的限制算子与逐行松弛过程结合在一起。对于笛卡尔均匀网格的情况，执行局部傅立叶分析。该方法针对不同的全张量系数问题和几个粗糙的四边形网格显示出鲁棒的收敛性。