Sending and Receiving on a Grid

In the most common cases, we want a full exchange of data between every two communicating processes. If we examine our schematic again

we will observe that we can think of the blue arrows as a sweep from left to right, while the orange arrows represent a return sweep from right to left. This pattern is particularly common when we are computing on a distributed domain and must exchange information among the subdomains.

Domain Decomposition

We have discussed domain decomposition in a general case. Let us now consider a more specific example. We wish to do some computations on a grid. A grid divides some region into smaller segments often called zones. We will convert our problem from some kind of continuous equations into a discretized system that will be solved on the grid.

The illustration shows a small 10x16 grid that we will divide into subgrids, one for each rank. To keep our first example simple, we will do a one-dimensional decomposition in which we will split the grid into strips.