Concepts: An object-oriented software package for partial differential equations

TLDR: This paper discusses an alternative way to approach the design challenge which it is called "concept oriented design", and applies this design methodology to Petrov-Galerkin methods leading to a class library for both, boundary element methods (BEM) and finite element Methods (FEM).

Abstract: Object oriented design has proven itself as a powerful tool in the field of scientific comput- ing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into classes such that the level of abstraction is essentially not raised. In this paper we discuss an alternative way to approach the design challenge which we call "concept oriented design". We apply this design methodology to Petrov-Galerkin methods leading to a class library for both, boundary element methods (BEM) and finite element methods (FEM). We show as a particular example the implementation of hp-FEM using the library with special attention to the handling of inconsistent meshes. Mathematics Subject Classification. 35-04, 65-04, 65N30, 65N50.