Variability of stencil computations for porous media.

Many problems formulated in partial differential equations lead to stencil-type structures after applying an appropriate structured discretization. On one hand, exploiting these stencil structures in simulations can lead to massive performance improvements, compared to forming a sparse matrix. On the other hand, the generality of the simulation is restricted, depending on the exact definition of the stencils. In this article, we discuss the variability of stencils in the domain of porous-media applications and present a family of models that grows in complexity. To demonstrate the relation between equation and discretization on the resulting stencil used to simulate the equation, we consider 4 models from the porous media domain. This way, we describe the influence of design decisions made during the discretization on the shape of stencils, to give application engineers' information on the variability they have to consider. This leads us to 2 variability models that shall help application engineers to understand the complexity and choices of stencil computations in the porous media domain.