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

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