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 th...