Towards an expressive language for PDE solvers

Abstract

Many significant real-life applications, e.g., air-craft design and environmental modelling, involve simulations based on the numerical solution of systems of time-dependent partial differential equations. In general, the computational domain has a complicated geometry, and the computations demand high-performance computers. The present paper lays a foundation for an expressive notation for this kind of application. By an object-oriented analysis concepts are identified, that can be combined flexibly enough to allow a programmer to express real computational problems (as opposed to model problems). The resulting concepts have been implemented as classes in C++. In a sense, this class library (referred to as Cogito/Solver) will specialize C++ into a language for the application domain under consideration. However, the aim is to use Cogito/Solver as a basis for higher-level interfaces. As a first attempt in this direction, an object-oriented database for Cogito/Solver objects has been implemented. Through an interface to this database, a programmer can compose an executable object (a Numerical Experiment), from various smaller objects, related to the different Cogito/Solver concepts.