This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov-Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12-26) and extends the convergence results form $\mathcal{O}(10^7)$ degrees of freedom (DOFs) to $\mathcal{O}(10^9)$ DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear dependence with respect to the wave frequency. The paper concludes with numerical results on hp-adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

翻译：---- 本文介绍了一个可扩展的多重网格预处理器，针对来自高频波算符的不连续Petrov-Galerkin（DPG）离散化的大规模系统。这项工作基于Petrides和Demkowicz的先前开发的多重网格预处理技术（计算和数学应用87（2021）pp. 12-26），并使用新的可扩展的并行MPI / OpenMP实现，将收敛结果从$ \mathcal {O}（10 ^ 7） $自由度（DOFs）扩展到$ \mathcal{O}（10 ^9）$自由度。本文的创新贡献包括一种基于细网格算子限制的粗网格系统的另一种定义，从而产生更好的收敛结果。在均匀细化设置中，提供了详细的收敛研究，证明了与波频线性相关的h和p稳健的收敛性。本文最后给出了hp适应性模拟的数值结果，包括高材料对比的大规模地震建模基准问题。