论文标题
$ p $ -Multilevel预先调查器，用于静态冷凝的Stokes方程
$p$-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation
论文作者
论文摘要
我们建议使用Stokes方程的混合高阶离散化（HHO）$ p $ - 多级预处理，并在数值上评估其在该方法的两个变体上的性能，并与经典的不连续的Galerkin方案进行比较。我们专门研究了$ p $ coarsening和静态冷凝的组合如何影响HHO $ V $循环迭代的性能。考虑了两种不同的静态冷凝程序，导致全局线性系统具有不同数量的未知数和非零元素。提出了一个有效的实现，即使用$ l^2 $ - 正交投影在网格面上定义的$ l^2 $ - 正交投影，并且对精细网格操作员的限制进行了递归且无矩阵的限制。各种分辨率策略在两维问题上得到了彻底验证。
We propose a $p$-multilevel preconditioner for Hybrid High-Order discretizations (HHO) of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical Discontinuous Galerkin scheme. We specifically investigate how the combination of $p$-coarsening and static condensation influences the performance of the $V$-cycle iteration for HHO. Two different static condensation procedures are considered, resulting in global linear systems with a different number of unknowns and non-zero elements. An efficient implementation is proposed where coarse level operators are inherited using $L^2$-orthogonal projections defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free. The various resolution strategies are thoroughly validated on two- and three-dimensional problems.
