Accelerating Geometric Multigrid Preconditioning with Half-Precision Arithmetic on GPUs

Abstract: 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.