Redundant Ghost Nodes in Jacobi

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

• Jacobis 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