Space-time waveform relaxation multigrid for Navier-Stokes

Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the resulting linear and nonlinear systems. In this work, we consider the all-at-once solution of the discretized Navier-Stokes equations over a space-time domain using waveform relaxation multigrid methods. In particular, we show how to extend spatial multigrid relaxation methods to a waveform relaxation method, and demonstrate the efficiency of the resulting monolithic Newton-Krylov-multigrid solver. Numerical results demonstrate the scalability of the solver for varying discretization order and physical parameters.