Stencil computations for PDE‐based applications with examples from DUNE and hypre. (24th February 2017) - Engwer, C.; Falgout, R. D.; Yang, U. M.
Summary: Stencils are commonly used to implement efficient on‐the‐fly computations of linear operators arising from partial differential equations. At the same time the term "stencil" is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend the software to enable stencil computations of more complex problems and methods such as inf‐sup‐stable Stokes discretizations and mixed finite element discretizations.