An abstraction for local computations on structured meshes and its extension to handling multiple materials

Computations involving a neighbourhood on structured meshes represents a wide class of applications that includes the simulation of cellular automata, and the solution of partial differential equations (PDEs). In this paper we present an abstraction for describing such computations at a high level, allowing fast experimentation and productivity. The abstraction is designed such that it can be automatically converted to various high-performance implementations. A critical feature of this abstraction is an extension to support a varying number of materials, or species, at each grid point, enabling much more complex simulations