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

Philipp Frauenfelder; Christian Lage

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 5, page 937-951
  • ISSN: 0764-583X

Abstract

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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 h p -FEM using the library with special attention to the handling of inconsistent meshes.

How to cite

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Frauenfelder, Philipp, and Lage, Christian. "Concepts—An object-oriented software package for partial differential equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.5 (2002): 937-951. <http://eudml.org/doc/245234>.

@article{Frauenfelder2002,
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.},
author = {Frauenfelder, Philipp, Lage, Christian},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {object oriented design; concept oriented design; $hp$-FEM; adaptivity; hp-FEM; Petrov-Galerkin methods; boundary element methods; finite-element methods},
language = {eng},
number = {5},
pages = {937-951},
publisher = {EDP-Sciences},
title = {Concepts—An object-oriented software package for partial differential equations},
url = {http://eudml.org/doc/245234},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Frauenfelder, Philipp
AU - Lage, Christian
TI - Concepts—An object-oriented software package for partial differential equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 5
SP - 937
EP - 951
AB - 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.
LA - eng
KW - object oriented design; concept oriented design; $hp$-FEM; adaptivity; hp-FEM; Petrov-Galerkin methods; boundary element methods; finite-element methods
UR - http://eudml.org/doc/245234
ER -

References

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  10. [10] C. Lage, Concept oriented design of numerical software. Technical Report 98-07, Seminar for Applied Mathematics, Swiss Federal Institute of Technology, Zürich (1998). 
  11. [11] A. Larsson, J. Henstridge et al., Dia. Internet (2001). http://www.lysator.liu.se/~alla/dia/ 
  12. [12] A.-M. Matache, Spectral and p -Finite Elements for problems with microstructure. Ph.D. thesis, Swiss Federal Institute of Technology, Zürich (2000). 
  13. [13] Object Management Group, Inc., Framingham, USA. OMG Unified Modeling Language Specification, 1.3 ed. (1999). http://www.rational.com/uml/resources/documentation/ 
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