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Redundant Ghost Nodes in Jacobi

Redundant Ghost Nodes in Jacobi. Overview of Memory Hierarchy Optimization Can be used on unstructured meshes Size of ghost region (and redundant computation) depends on network/memory speed vs. computation. To compute green. Copy yellow. Compute blue.

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Redundant Ghost Nodes in Jacobi

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  1. Redundant Ghost Nodes in Jacobi • Overview of Memory Hierarchy Optimization • Can be used on unstructured meshes • Size of ghost region (and redundant computation) depends on network/memory speed vs. computation To compute green Copy yellow Compute blue

  2. Convergence of Nearest Neighbor Methods • Jacobi’s method involves nearest neighbor computation on nxn grid (N = n2) • So it takes O(n) = O(sqrt(N)) iterations for information to propagate • E.g., consider a rhs (b) that is 0, except the center is 1 • The exact solution looks like: Even in the best case, any nearest neighbor computation will take n/2 steps to propagate on an nxn grid

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