Optimal tilings for iterative PDE solvers

A simple, universal procedure for deriving the optimal partition for a given iterative partial differential equation (PDE) algorithm is presented. A previous analysis is extended to include geometrical considerations-in particular, the relative orientation of the update stencil and the partition tile. On the basis of this procedure, two new partitionings are derived for specific PDE algorithms which are more efficient than any previously known. The choice of partition is found to be independent of the details of the multiprocessor architecture for a wide range of operating parameters.<
>