Treffer: Multilevel Interior Penalty Methods on GPUs.

We present a matrix-free multigrid method for high-order Discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are optimized through localization and fast diagonalization techniques. Leveraging conflict-free access patterns in shared memory, arithmetic throughput of up to 40% of the peak performance on NVIDIA A100 GPUs are achieved. Experimental results affirm the effectiveness of mixed-precision approaches and Message Passing Interface (MPI) parallelization in accelerating algorithms. Furthermore, an assessment of solver efficiency and robustness is provided across both two and three dimensions, with applications to Poisson problems. [ABSTRACT FROM AUTHOR]

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