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