DUNE-FEM. A general purpose discretization toolbox for parallel and adaptive scientific computing

DUNE-FEM is a free discretization toolbox for parallel and adaptive scientific computing based on DUNE. The implementation of discretization schemes such as finite elements, finite volumes or discontinuous Galerkin schemes is based on abstractions that are very close to the mathematical description of the underlying methods. In this contribution we will give a compact overview on the design and abstraction principles of DUNE-FEM and demonstrate its wide range of applicability in numerical experiments ranging from the solution of flow processes on surfaces to parallel and adaptive fluid flow in three space dimensions. A more detailed presentation of the abstraction principles is given in [Dedner et al. A generic interface for parallel and adaptive discretization scheme: abstraction principles and the Dune-Fem module. Computing 90 (2010), no. 3-4, 165–196]. In the whole design of DUNE-FEM efficiency was a main concern. In this paper we will give some indication to what degree the generic programming principals used in DUNE-FEM can lead to the generation of efficient code.