Decomposition

• Look for concurrency in loop iterations
  • In this case iterations are really dependent
  • Iteration ( i , j) depends on iterations ( i , j-1) and (i-1, j)

• Each anti-diagonal can be computed in parallel
• Must synchronize after each anti-diagonal (or pt-to-pt)
• Alternative: red-black ordering (different update pattern)

• Can update all red points first, synchronize globally with a barrier and then update all black points
  • May converge faster or slower compared to sequential program
  • Converged equilibrium may also be different if there are multiple solutions
  • Ocean simulation uses this decomposition
• We will ignore the loop-carried dependence and go ahead with a straight-forward loop decomposition
  • Allow updates to all points in parallel
  • This is yet another different update order and may affect convergence
  • Update to a point may or may not see the new updates to the nearest neighbors (this parallel algorithm is non-deterministic)