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条件器，旨在求解由高频波动算子的不连续Petrov-Galerkin（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条件技术（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：基于精细网格算子限制的粗网格系统替代定义，从而获得了更优的收敛结果。在均匀网格细化设置下，本文提供了详细的收敛性研究，证明了h和p意义上的稳健收敛性，以及收敛性对波频率的线性依赖关系。文章最后展示了hp自适应模拟的数值结果，其中包括一个具有高材料对比度的大规模地震模型基准测试问题。