Mixed-Precision GPU-Multigrid Solvers with Strong Smoothers

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We present efficient parallelisation strategies for geometric multigrid solvers on GPUs. Such solvers are a fundamental building block in the solution of PDE problems using discretisation techniques like finite elements, finite differences and finite volumes. Both generalised tensor product meshes and unstructured meshes are considered. Special focus is placed on numerically strong smoothers, which are challenging to parallelise due to their inherently sequential, recursive character. We address the inherent trade-off between numerical and hardware performance, i.e., between global coupling and degree of parallelism. To further improve performance, a mixed precision strategy is applied. By carefully balancing these contradictory requirements, we achieve more than an order of magnitude speedup over highly optimised CPU code.