New Geometric Immersed Interface Multigrid Solvers
New Geometric Immersed Interface Multigrid Solvers
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DOI：
10.1137/s1064827503421707
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发表时间：
2004-05
期刊：
影响因子：
--
通讯作者：
L. Adams;T. Chartier
中科院分区：
文献类型：
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作者：
L. Adams;T. Chartier
在[L.亚当斯和Z. Li，SIAM J. Sci.计算：24（2002），pp. 463--479]中，多重网格方法被专门设计用于已经使用其中描述的方法离散化的界面问题，并且在[Z. Li和K. Ito，SIAM J. Sci.计算：23（2001），pp. 339--361]的最大值原理保持格式的椭圆界面问题。本文对该方法进行了改进，对浸入界面附近的网格点给出了一种新的约束条件，保证了粗网格矩阵是M矩阵。我们比较了这种新的限制器注入和插值转置。我们表明，V-周期的数量是恒定的网格尺寸减小，增加只有轻微的不连续的问题系数的比例增长的接口，只有当使用这种新的限制器。
In [L. Adams and Z. Li, SIAM J. Sci. Comput., 24 (2002), pp. 463--479], a multigrid method was designed specifically for interface problems that have been discretized using the methods described therein, and in [Z. Li and K. Ito, SIAM J. Sci. Comput., 23 (2001), pp. 339--361] for elliptic interface problems using the maximum principle preserving schemes. In this paper, we improve on this method by giving a new interpolator for grid points near the immersed interface and a new restrictor that guarantees the coarse-grid matrices are M-matrices. We compare this new restrictor to injection and the transpose of interpolation. We show that the number of V-cycles is constant as the mesh size decreases and increases only slightly as the ratio of the discontinuous problem coefficient grows at the interface only when this new restrictor is used.