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

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning high-order finite element problems. The methods described here allow construction effective preconditioners problems with optimal memory usage computational complexity. are based on a spectrally equivalent low-order discretization refined mesh, which is then amenable to, example, algebraic multigrid preconditioning. constants equivalence independent mesh size polynomial degree. For vector in H(curl) H(div) (e.g., electromagnetic or radiation diffusion problems), specially constructed interpolation–histopolation basis used to ensure fast convergence. Detailed performance studies carried out analyze efficiency algorithms. kernel throughput each main algorithmic components measured, strong weak parallel scalability demonstrated. different relative weighting significance GPUs CPUs discussed. Results involving adaptively nonconforming meshes shown, use large-scale magnetic problem using all spaces de Rham complex illustrated.