Multilevel Interior Penalty Methods on GPUs

Cu Cui; Guido Kanschat

doi:10.1145/3765616

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arXiv · 2405.18982

Multilevel Interior Penalty Methods on GPUs

Cu Cui·Guido Kanschat

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Abstract

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 39% of the peak performance on Nvidia A100 GPUs are achieved. Experimental results affirm the effectiveness of mixed-precision approaches and 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.

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Cu Cui, Guido Kanschat. 2024-05-29. Multilevel Interior Penalty Methods on GPUs. https://doi.org/10.1145/3765616

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