Research Article

Concepts—An Object-Oriented Software Package for Partial Differential Equations

Frauenfelder, Philipp^a1 and Lage, Christian^a2

^a1 Seminar for Applied Mathematics, Swiss Federal Institute of Technology, 8092 Zürich, Switzerland. pfrauenf@math.ethz.ch.

^a2 372 Funston Avenue, San Francisco, CA 94118, USA. cl@numiracle.com.

Abstract

Object oriented design has proven itself as a powerful tool in the field of scientific computing. 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.

(Received December 17 2001)

(Revised May 21 2002)

(Online publication October 15 2002)

Key Words:

• Object oriented design;
• concept oriented design;
• hp-FEM;
• adaptivity.

Mathematics Subject Classification:

• 35-04;
• 65-04;
• 65N30;
• 65N50