论文标题
不连续的Galerkin方法的统一子空间校正前校正预处理用$ hp $ - 进行
Uniform subspace correction preconditioners for discontinuous Galerkin methods with $hp$-refinement
论文作者
论文摘要
在本文中，我们为不连续的Galerkin（DG）离散椭圆形问题开发了子空间校正预处理。这些预调节器基于DG有限元空间的分解成一个符合的子空间和一组小的不合格边缘空间。使用无基质的低阶技术对符合的子空间进行了预处理，在这项工作中，我们使用各种限制方法扩展到$ hp $ - 重新启动上下文。所得线性系统的条件数与网状$ h $的粒度和多项式近似$ p $的程度无关。该方法可与多项式程度的任何程度不规则性和任意分布一起使用。数值示例显示在涉及对称内部惩罚方法和Bassi和Rebay的第二种方法（BR2）的几个涉及自适应和随机精制网格的测试用例（BR2）。
In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with $hp$-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work we extend to the $hp$-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh $h$, and the degree of polynomial approximation $p$. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).
