  With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs,
high-performance computing applications can benefit from lower precision at
appropriate spots to speed up the overall execution time. In this paper, we
investigate a mixed-precision geometric multigrid method to solve large sparse
systems of equations stemming from discretization of elliptic PDEs. While the
final solution is always computed with high-precision accuracy, an iterative
refinement approach with multigrid preconditioning in lower precision and
residuum scaling is employed. We compare the FP64 baseline for Poisson's
equation to purely FP16 multigrid preconditioning and to the employment of
FP16-FP32-FP64 combinations within a mesh hierarchy. While the iteration count
is almost not affected by using lower accuracy, the solver runtime is
considerably decreased due to the reduced memory transfer and a speedup of up
to 2.5x is gained for the overall solver. We investigate the performance of
selected kernels with the hierarchical Roofline model.
