Isomorphic, Sparse MPI-like Collective Communication Operations for Parallel Stencil Computations

We propose a specification and discuss implementations of collective operations for parallel stencil-like computations that are not supported well by the current MPI 3.1 neighborhood collectives. In our isomorphic, sparse collectives all processes partaking in the communication operation use similar neighborhoods of processes with which to exchange data. Our interface assumes the p processes to be arranged in a d-dimensional torus (mesh) over which neighborhoods are specified per process by identical lists of relative coordinates. This extends significantly on the functionality for Cartesian communicators, and is a much lighter mechanism than distributed graph topologies. It allows for fast, local computation of communication schedules, and can be used in more dynamic contexts than current MPI functionality. We sketch three algorithms for neighborhoods with s source and target neighbors, namely a) a direct algorithm taking s communication rounds, b) a message-combining algorithm that communicates only along torus coordinates, and c) a message-combining algorithm using between [log s] and [log p] communication rounds. Our concrete interface has been implemented using the direct algorithm a). We benchmark our implementations and compare to the MPI neighborhood collectives. We demonstrate significant advantages in set-up times, and comparable communication times. Finally, we use our isomorphic, sparse collectives to implement a stencil computation with a deep halo, and discuss derived datatypes required for this application.