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 from $\mathcal{O}(10^7)$ 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：本文提出了一种可扩展的多重网格预处理方法，针对高频波动算子间断佩特罗夫-伽辽金（DPG）离散化所产生的大规模系统。本研究基于Petrides和Demkowicz先前开发的多重网格预处理技术（Comput. Math. Appl. 87 (2021) pp. 12-26），并通过一种新的可扩展并行MPI/OpenMP实现，将收敛性结果从$\mathcal{O}(10^7)$自由度扩展至$\mathcal{O}(10^9)$自由度。本文的创新贡献包括：基于细网格算子限制的粗网格系统替代性定义，从而获得了更优的收敛性结果。在均匀细化设定下，本文提供了详细的收敛性研究，证明了h和p鲁棒收敛性以及与波动频率的线性依赖关系。最后，本文给出了hp自适应模拟的数值结果，包括一个具有高材料对比度的大规模地震建模基准问题。