Optimizing Stencil Computations : Multicore-optimized Wavefront Diamond Blocking on Shared and Distributed Memory Systems

Iterative Stencil Computations (ISC) appear in wide variety of scientific applications, partial differential equation (PDE) solvers being the most important one. In iterative stencil computations, each point in a multi-dimensional spatial grid is updated using weighted contributions from its neighbor points, defined by the stencil operator. The stencil operator specifies the relative coordinates of the contributing points and their weights. The weights can be constant or variable with some or no symmetry around the updated point. Depending on the discretization order, the radius of the stencil operator may also vary. The grid update operation over the spatial domain (“sweep”) is usually repeated many times (time steps) until some convergence criterion is met.