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With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs,high-performance computing applications can benefit from lower precision atappropriate spots to speed up the overall execution time. In this paper, weinvestigate a mixed-precision geometric multigrid method to solve large sparsesystems of equations stemming from discretization of elliptic PDEs. While thefinal solution is always computed with high-precision accuracy, an iterativerefinement approach with multigrid preconditioning in lower precision andresiduum scaling is employed. We compare the FP64 baseline for Poisson'sequation to purely FP16 multigrid preconditioning and to the employment ofFP16-FP32-FP64 combinations within a mesh hierarchy. While the iteration countis almost not affected by using lower accuracy, the solver runtime isconsiderably decreased due to the reduced memory transfer and a speedup of upto 2.5x is gained for the overall solver. We investigate the performance ofselected kernels with the hierarchical Roofline model.

Accelerating Geometric Multigrid Preconditioning with Half-Precision Arithmetic on GPUs