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.

翻译：本文提出了一种高效的黑箱型多重网格方法，用于求解逻辑矩形网格上达西问题的多点通量逼近。该方法基于单元中心型多重网格算法，结合了分片常数插值与Wesseling/Khalil限制算子，并采用线型松弛过程。针对笛卡尔均匀网格情形进行了局部傅里叶分析。数值实验表明，该方法对不同全张量系数问题及多种粗糙四边形网格均展现出稳健的收敛性。