  We present a matrix-free multigrid method for high-order discontinuous
Galerkin (DG) finite element methods with GPU acceleration. A performance
analysis is conducted, comparing various data and compute layouts. Smoother
implementations are optimized through localization and fast diagonalization
techniques. Leveraging conflict-free access patterns in shared memory,
arithmetic throughput of up to 39% of the peak performance on Nvidia A100 GPUs
are achieved. Experimental results affirm the effectiveness of mixed-precision
approaches and MPI parallelization in accelerating algorithms. Furthermore, an
assessment of solver efficiency and robustness is provided across both two and
three dimensions, with applications to Poisson problems.
