论文标题
表面上快速辅助空间预处理
Fast auxiliary space preconditioners on surfaces
论文作者
论文摘要
这项工作为离散的拉普拉斯 - 贝特拉米操作员介绍了Hypersurfaces的统一预处理。特别是，在快速辅助空间预处理（FASP）的框架内，我们为拉普拉斯 - 贝特拉米类型方程开发了有效且用户友好的多层次预处理，由Lagrange，不合格的线性和不连续的Galerkin Elements离散。该分析适用于在封闭表面上的半定准则问题。提出了在2D表面和3D高空的数字实验，以说明所提出的预处理的效率。
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning (FASP), we develop efficient and user-friendly multilevel preconditioners for the Laplace--Beltrami type equation discretized by Lagrange, nonconforming linear, and discontinuous Galerkin elements. The analysis applies to semi-definite problems on a closed surface. Numerical experiments on 2d surfaces and 3d hypersurfaces are presented to illustrate the efficiency of the proposed preconditioners.
