Multilevel Interior Penalty Methods on GPUs

2024/05/29 by Cui, Cu, Kanschat, Guido · 1 citation
#65N55 #65Y20 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2405.18982

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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• A Geometric Multigrid Preconditioner for Discontinuous Galerkin Shifted Boundary Method

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