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Mixed-Dimensional Auxiliary Space Preconditioners
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-10-22 , DOI: 10.1137/19m1292618
Ana Budiša , Wietse M. Boon , Xiaozhe Hu

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A3367-A3396, January 2020.
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the use of conforming mixed finite element spaces, we then expand these results to the discrete case and obtain a decomposition in terms of nodal Lagrange elements. In turn, nodal preconditioners are proposed analogous to the auxiliary space preconditioners of Hiptmair and Xu [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509]. Numerical experiments show the performance of this preconditioner in the context of flow in fractured porous media.


中文翻译:

混合维辅助空间预处理器

SIAM科学计算杂志,第42卷,第5期,第A3367-A3396页,2020年1月。
这项工作介绍了用于混合维偏微分方程离散化的节点辅助空间预处理器。我们首先考虑连续设置,并将常规分解推广到该设置。通过使用一致的混合有限元空间,然后将这些结果扩展到离散情况,并获得关于节点拉格朗日元素的分解。继而,提出了类似于Hiptmair和Xu的辅助空间预处理器的节点预处理器[SIAM J. Numer。,《分析》,第45卷,2007年,第2483--2509页]。数值实验表明该预处理器在破裂的多孔介质中流动的情况下的性能。
更新日期:2020-12-04
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