Black Box Multigrid with coarsening by a factor of three
Black Box Multigrid with coarsening by a factor of three
复制标题
粗化三倍的黑盒多重网格
DOI：
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发表时间：
2010
影响因子：
4.3
通讯作者：
J. Moulton
中科院分区：
文献类型：
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作者：
J. Dendy;J. Moulton
黑盒多重网格（BoxMG）是一个强大的变分多重网格求解扩散方程的逻辑结构网格。BoxMG标准品使用了两倍的粗化。它通过将单元中心视为待粗化的未知量来处理逻辑矩形网格上的单元中心离散化。这样的策略不能保持细胞结构。也就是说，粗网格单元不是细网格单元的并集。在某些应用中，例如局部网格细化，需要保留单元结构。在本文中，我们开发了一种方法，采用粗化的三个因素。它是标准BoxMG的自然推广，使用算子诱导插值（近似保持法向通量的连续性），限制为插值的转置，以及Galerkin粗化。此外，我们引入了一个新的彩色块高斯-赛德尔计划，这是出于形式的插值算子，被称为“图案”放松。我们提出的数值结果表明，这种方法的鲁棒性不连续的扩散系数，边界条件和网格尺寸。出版社：John Wiley & Sons，Ltd
Black Box Multigrid (BoxMG) is a robust variational multigrid solver for diffusion equations on logically structured grids. BoxMG standardly uses coarsening by a factor of two. It handles cell‐centered discretizations on logically rectangular grids by treating the cell‐centers as the unknowns to be coarsened. Such a strategy does not preserve the cell structure. That is, coarse‐grid cells are not the union of fine‐grid cells. In some applications, such as local grid refinement, it is desirable that the cell structure be preserved. In this paper, we develop a method that employs coarsening by a factor of three. It is a natural generalization of standard BoxMG, using operator‐induced interpolation (which approximately preserves the continuity of the normal flux), restriction as the transpose of interpolation, and Galerkin coarsening. In addition, we introduce a new colored block Gauss–Seidel scheme that is motivated by the form of the interpolation operator, dubbed ‘pattern’ relaxation. We present numerical results that demonstrate robustness of this method with respect to discontinuous diffusion coefficients, boundary conditions, and grid dimension. Published in 2010 by John Wiley & Sons, Ltd.