CMOR Publications

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CMOR Faculty Publications

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Browsing CMOR Publications by Author "Adams, Mark F."

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    Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures
    (Society for Industrial and Applied Mathematics, 2017) Adams, Mark F.; Hirvijoki, Eero; Knepley, Matthew G.; Brown, Jed; Isaac, Tobin; Mills, Richard
    The Landau collision integral is an accurate model for the small-angle dominated Coulomb collisions in fusion plasmas. We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear multispecies Landau integral with adaptive mesh refinement using the PETSc library (ŭlwww.mcs.anl.gov/petsc). We develop algorithms and techniques to efficiently utilize emerging architectures with an approach that minimizes memory usage and movement and is suitable for vector processing. The Landau collision integral is vectorized with Intel AVX-512 intrinsics and the solver sustains as much as 22% of the theoretical peak flop rate of the Second Generation Intel Xeon Phi (``Knights Landing'') processor.
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    Segmental refinement: A multigrid technique for data locality
    (Society for Industrial and Applied Mathematics, 2016) Adams, Mark F.; Brown, Jed; Knepley, Matthew G.; Samtaney, Ravi
    We investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. We present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.