A virtual topology is a mechanism for naming the processes in a communicator in a way that fits the communication pattern better.

• The main goal is to make programming simpler.

• It may also provide hints to the run-time system which allow it to optimize communication.

• For example: if your processes will communicate mainly with the nearest neighbors (see the 2-D grid in the figure below), you could create a topology to reflect this.
  • The following 2-D grid is a virtual topology of 12 processes. The lines denote the main communication patterns, namely between neighbors. The grid actually has a cyclic boundary condition in one direction, e.g. process 0 and 9 are "connected". The top numbers represent the ranks in the new communicator and the conceptual coordinates mapped to the ranks.

    

• What this buys is access to convenient routines which, for example, compute the ranks of your nearest neighbor given its coordinates in the grid. When doing this one needs to pay attention to the boundary conditions, i.e. returning MPI_NULL_PROC if you go outside the grid.

• Although the main communication patterns are highlighted by "connection lines", any process within the communicator can still communicate with any other.