A Scalable, Efficient Scheme for Evaluation of Stencil Computations over Unstructured Meshes

James King, Robert M. Kirby
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT
IEEE SuperComputing, 2013

   title={A Scalable, Efficient Scheme for Evaluation of Stencil Computations over Unstructured Meshes},

   author={King, James and Kirby, Robert M},



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Stencil computations are a common class of operations that appear in many computational scientific and engineering applications. Stencil computations often benefit from compile-time analysis, exploiting data-locality, and parallelism. Post-processing of discontinuous Galerkin (dG) simulation solutions with B-spline kernels is an example of a numerical method which requires evaluating computationally intensive stencil operations over a mesh. Previous work on stencil computations has focused on structured meshes, while giving little attention to unstructured meshes. Performing stencil operations over an unstructured mesh requires sampling of heterogeneous elements which often leads to inefficient memory access patterns and limits data locality/reuse. In this paper, we present an efficient method for performing stencil computations over unstructured meshes which increases data-locality and cache efficiency, and a scalable approach for stencil tiling and concurrent execution. We provide experimental results in the context of post-processing of dG solutions that demonstrate the effectiveness of our approach.
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