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1 results

  • 4 - Parallel Stencils

  • Richard Ansorge, University of Cambridge
  • Book:
    Programming in Parallel with CUDA
    Published online:
    04 May 2022
    Print publication:
    02 June 2022, pp 106-141

  • Summary

    The solution of partial differential equations in two and three-dimensions using stencil iteration (Jacobi’s method) is discussed and illustrated for Laplace’s equation. A very simple kernel gives about a factor of 100 speed-up compared to the host CPU.The very slow convergence of the Jacobi method can be addressed by using solutions on lower resolution grids to initialise higher resolution grids. A convergence check using the maximum change per iteration is also illustrated. Digital image processing is another example of stencil use and a number of digital image filters are shown including the Sobel filter for edge finding and the median filter for noise reduction. The fast GPU-based median filter uses one thread per image pixel and is implemented using an optimal Batcher network.