2016/07/14 by Matthew G. Knepley, Knepley, Matthew G., Karl Rupp +3 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #FOS: Computer and information sciences #Fluid Dynamics Simulations and Interactions #G.1.8 #G.4 #Mathematical Software (cs.MS) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1607.04245
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call thread transposition to avoid reductions while vectorizing aggressively. On the NVIDIA GTX580, which has a nominal single precision peak flop rate of 1.5 TF/s and a memory bandwidth of 192 GB/s, we achieve close to 300 GF/s for element integration on first-order discretization of the Laplacian operator with variable coefficients in two dimensions, and over 400 GF/s in three dimensions. From our performance model we find that this corresponds to 90% of our measured achievable bandwidth peak of 310 GF/s. Further experimental results also match the predicted performance when used with double precision (120 GF/s in two dimensions, 150 GF/s in three dimensions). Results obtained for the linear elasticity equations (220 GF/s and 70 GF/s in two dimensions, 180 GF/s and 60 GF/s in three dimensions) also demonstrate the applicability of our method to vector-valued partial differential equations.