On Object-Oriented Frameworks and Coordinate Free Formulations of PDEs

An object-oriented (OO) framework for Partial tial Equations (PDEs) provides software abstractions for numerical simulation of PDEs. The design of such frameworks is not trivial, and the outcome of the design is highly t on which mathematical abstractions one chooses rt. In this paper, coordinate free abstractions for PDEs are advocated. The coordinate free formulation of a PDE hides the underlying coordinate system. Therefore, software based on these concepts has the prospect of being more modular, since the PDE formulation is separated from the representation of the coordinates. Use of coordinate free methods in two independent OO frameworks are presented, in order to exemplify the viability of the concepts. The described applications simulate seismic waves for various classes of rock models and the incompressible Navier-Stokes equations on curvi-linear grids, respectively. In both cases, the possibility to express the equations in a domain independent fashion is crucial. Similaritie...

• Type: Journal
• Year: 2002
• Where: EWC
• Authors: Magne Haveraaen, Hans Z. Munthe-Kaas, Krister Åhlander
• Keywords: Coordinate Free Formulation, EWC 2002, Partial Tial Equations, PDEs