In this work, we investigate the performance of -multilevel preconditioners for discontinuous Galerkin (dG) discretisations of elliptic operators with constant coefficients. Recent publications targeting multilevel solution strategies for incompressible fluid flow computations demonstrated that dG discretisation of viscous terms require ad hoc inherited multilevel preconditioners. Accordingly, we consider elliptic operators discretised by means of the BR2 dG method introduced by Bassi and Rebay and we compare agglomeration-based hp-coarsening with previously introduced -multilevel strategies. The numerical results show that, when the polynomial degree is sufficiently high and the mesh is sufficiently dense, the hp-multilevel preconditioner can be fruitfully exploited.

中文翻译：

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{hp-hp}-椭圆算子的多级不连续伽辽金解策略

在这项工作中，我们研究了 - 多级预处理器对具有常数系数的椭圆算子的不连续 Galerkin (dG) 离散化的性能。最近针对不可压缩流体流动计算的多级求解策略的出版物表明，粘性项的 dG 离散化需要特别继承的多级预处理器。因此，我们考虑通过 Bassi 和 Rebay 引入的 BR2 dG 方法离散化的椭圆算子，并将基于凝聚的 hp 粗化与之前引入的多级策略进行比较。数值结果表明，当多项式次数足够高且网格足够密集时，可以有效地利用 hp 多级预处理器。