On concepts of PDE-Software: The cellwise oriented approach in DEAL

In this note, we review and refine our concepts of a cellwise oriented approach to PDE-software described in the dissertations of G. Kanschat and F.T. Suttmeier. The problem of non-matching cells in finite element discretisations on locally refined meshes is adressed. General concepts of the treatment of so-called hanging nodes are illustrated at the standard bilinear and -quadratic FE-spaces. These results carry over to nonconforming elements. Furthermore, two features we focus on are on one hand the significant reduction of memory requirements employing local scaling techniques for representing operators. The second aspect is data locality, which is the basis for vectorisation/parallelisation and for employing efficient cache-optimised hardware-techniques. We illustrate our ideas and provide numerical results by treating a standard benchmark problem (disc with a hole) from structural mechanics. Mathematics Subject Classification: 65N50, 65N99