  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.
