A partitioning strategy for explicit difference methods (Q921877)

Two different partition shapes, slices and rectangles, are analyzed for the case of explicit difference methods on regular grids. Two different work factors are assumed, \({\mathcal W}_ I\) at interior points and \({\mathcal W}_ B\) at boundary points. It is shown that a good strategy is to nevertheless do the partitioning as if the work was equal at all points. This strategy is nearly optimal, in the sense that it will in most cases give only a small reduction of the efficiency. An algorithm which simplifies the choice of partition shape for problems with different work factors is suggested. The algorithm has been implemented in a computer program. It is remarked that the algorithm should not be applied if \({\mathcal W}_ B\) is much larger than \({\mathcal W}_ I\).