Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods
Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods
复制标题
用于高阶无矩阵连续和不连续伽辽金方法的高效低阶细化预处理器
DOI：
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发表时间：
2019
影响因子：
3.1
通讯作者：
Will Pazner
中科院分区：
文献类型：
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作者：
Will Pazner
本文基于FEM-SEM等价和可加性Schwarz方法，设计了椭圆型问题高阶连续和不连续Galerkin离散无矩阵解的预条件。在不形成系统矩阵的情况下使用高阶算子，利用和分解进行高效求值。采用谱等效低阶有限元算子在精细网格上进行离散预处理。低阶精细化网格是各向异性的，在$p$中形状不规则，需要专门的求解器来处理各向异性。我们使用了一个结构化的几何多网格v循环和有序的ILU(0)平滑。通过在$h$和$p$上具有鲁棒性的重叠加性Schwarz方法对预条件进行并行化。将该方法推广到内部惩罚和BR2不连续Galerkin离散，在惩罚参数的大小上也具有鲁棒性。给出了各种算例的数值结果，验证了预调节器的均匀性。
In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in $p$, requiring specialized solvers to treat the anisotropy. We make use of a structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in $h$ and $p$. The method is extended to interior penalty and BR2 discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.
与 LegendreâGaussâLobatto 网格关联的嵌套二进网格
影响因子：
2.1
作者：
Kolja Brix;Claudio Canuto;Wolfgang Dahmen
通讯作者：
Wolfgang Dahmen