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In this paper, we present algorithms and implementations for the end-to-endGPU acceleration of matrix-free low-order-refined preconditioning of high-orderfinite element problems. The methods described here allow for the constructionof effective preconditioners for high-order problems with optimal memory usageand computational complexity. The preconditioners are based on the constructionof a spectrally equivalent low-order discretization on a refined mesh, which isthen amenable to, for example, algebraic multigrid preconditioning. Theconstants of equivalence are independent of mesh size and polynomial degree.For vector finite element problems in $H({\rm curl})$ and $H({\rm div})$ (e.g.for electromagnetic or radiation diffusion problems) a specially constructedinterpolation-histopolation basis is used to ensure fast convergence. Detailedperformance studies are carried out to analyze the efficiency of the GPUalgorithms. The kernel throughput of each of the main algorithmic components ismeasured, and the strong and weak parallel scalability of the methods isdemonstrated. The different relative weighting and significance of thealgorithmic components on GPUs and CPUs is discussed. Results on problemsinvolving adaptively refined nonconforming meshes are shown, and the use of thepreconditioners on a large-scale magnetic diffusion problem using all spaces ofthe finite element de Rham complex is illustrated.

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations