SIAM Journal on Scientific Computing, Ahead of Print.
We consider a second-order elliptic PDE discretized by the hybrid high-order method, for which globally coupled unknowns are located at faces. To efficiently solve the resulting linear system, we propose a geometric multigrid algorithm that keeps the degrees of freedom on the faces at every grid level. The core of the algorithm lies in the design of the prolongation operator that passes information from coarse to fine faces through the reconstruction of an intermediary polynomial of higher degree on the cells. High orders are natively handled by the use of the same polynomial degree at every grid level. The proposed algorithm requires a hierarchy of nested meshes, such that the faces (and not only the elements) are successively coarsened. Numerical tests on homogeneous and heterogeneous diffusion problems show fast convergence, scalability in the mesh size and polynomial order, and robustness with respect to heterogeneity of the diffusion coefficient.

中文翻译：

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混合高阶离散化的 H 多重网格方法

SIAM 科学计算杂志，提前印刷。
我们考虑通过混合高阶方法离散的二阶椭圆偏微分方程，其中全局耦合未知数位于面。为了有效地解决由此产生的线性系统，我们提出了一种几何多重网格算法，该算法在每个网格级别上保持面部的自由度。该算法的核心在于延长算子的设计，通过在细胞上重建更高阶的中间多项式，将信息从粗面到细面传递。通过在每个网格级别使用相同的多项式次数，本机处理高阶。所提出的算法需要嵌套网格的层次结构，从而使面（不仅是元素）连续粗化。对同质和异质扩散问题的数值测试表明收敛速度快，