Vertex-based auxiliary space multigrid method and its application to linear elasticity equations

：李佳音（兰州大学）
：2025-10-28 16:30
：海韵园实验楼S102

报告人：李佳音（兰州大学）

时  间：2025年10月28日16:30

地  点：海韵园实验楼S102

内容摘要:

In this talk, a vertex-based auxiliary space multigrid (V-ASMG) method as a preconditioner of the PCG method is proposed for solving the large sparse linear equations derived from the linear elasticity equations. The main key of such V-ASMG method lies in an auxiliary region-tree structure based on the geometrically regular subdivision. The computational complexity of building such a region-tree is O (qN log2 N ), where N is the number of the given original grid vertices and q is the power of the ratio of the maximum distance d_max to minimum distance d_min between the given original grid vertices. The process of constructing the auxiliary region-tree is similar to the method in [L. Grasedyck, L. Wang, J.C. Xu, Numerische Mathematik, 2016], but the selection of the representative points is changed. To be more specific, instead of choosing the barycenters, the correspondence between each grid layer is constructed based on the position relationship of the grid vertices. There are two advantages for this approach: the first is its simplicity, there is no need to deal with hanging points when building the auxiliary region-tree, and it is possible to construct the restriction/prolongation operator directly by using the bilinear interpolation function, and it is easy to be generalized to other problems as well, due to all the information we need is only the grid vertices; the second is its strong convergence, the corresponding relative residual can quickly converge to the given tolerance(It is taken to be 10^−6 in this paper), thus obtaining the desired numerical solution. Two- and three-dimensional numerical experiments are given to verify the strong convergence of the proposed V-ASMG method as a preconditioner of the PCG method.

个人简介：

李佳音，兰州大学数学与统计学院副教授。她于2023年获得厦门大学数学科学学院计算数学博士学位，博士导师邱建贤教授，联合培养博士导师舒其望教授。李佳音毕业之后于北京大学和北京大学重庆大数据研究院做联合博士后，从事有限元工业软件北达飞易的开发工作，主要负责多重网格快速算法框架搭建，合作导师胡俊教授。在站期间主持中国博士后科学基金面上项目1项和特别资助1项。李佳音的研究兴趣主要集中在双曲守恒律的高阶数值格式设计、多重网格快速算法等方向。相关结果发表在《Journal of Computational Physics》、《Communications in Computational Physics》等。

 

联系人：赵状