cs140-stencilmeshgraph

# cs140-stencilmeshgraph - Computation on Computation meshes...

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Computation on Computation on meshes, meshes, sparse matrices, sparse matrices, and graphs and graphs Some slides are from David Culler, Jim Demmel, Bob Lucas, Horst Simon, Kathy Yelick, et al., UCB CS267

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2 Parallelizing Stencil Computations Parallelizing Stencil Computations Parallelism is simple Grid is a regular data structure Even decomposition across processors gives load balance Spatial locality limits communication cost Communicate only boundary values from neighboring patches Communication volume v = total # of boundary cells between patches
3 Two-dimensional block decomposition Two-dimensional block decomposition n mesh cells, p processors Each processor has a patch of n/p cells Block row (or block col) layout: v = 2 * p * sqrt(n) 2-dimensional block layout: v = 4 * sqrt(p) * sqrt(n)

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4 Ghost Nodes in Stencil Computations Ghost Nodes in Stencil Computations Comm cost = α * (#messages) + β * (total size of messages) Keep a ghost copy of neighbors’ boundary nodes Communicate every second iteration , not every iteration Reduces #messages, not total size of messages Costs extra memory and computation Can also use more than one layer of ghost nodes Gr e e n = my i nt e r i or node s Ye l l ow = ne i ghbor s ’ boundar y node s = my “ghos t node s ” Bl ue = my boundar y node s
5 Parallelism in Regular meshes Parallelism in Regular meshes Computing a Stencil on a regular mesh need to communicate mesh points near boundary to neighboring processors. Often done with ghost regions Surface-to-volume ratio keeps communication down, but Still may be problematic in practice Implemented using “ghost” regions. Adds memory overhead

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6 Irregular mesh: NASA Airfoil in 2D Irregular mesh: NASA Airfoil in 2D
7 Composite Mesh from a Mechanical Structure Composite Mesh from a Mechanical Structure

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8 Adaptive Mesh Refinement (AMR) Adaptive Mesh Refinement (AMR) Adaptive mesh around an explosion Refinement done by calculating errors
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cs140-stencilmeshgraph - Computation on Computation meshes...

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