Case Study on Algebraic Software Methodologies for Scientific Computing

Abstract

The use of domain specific languages and appropriate software architectures are currently seen as the way to enhance reusability and improve software productivity. Here we outline a use of algebraic software methodologies and advanced program constructors to improve the abstraction level of software for scientific computing. This leads us to the language of coordinate free numerics as an alternative to the traditional coordinate dependent array notation. This provides the backdrop for the three accompanying papers:Coordinate Free Programming of Computational Fluid Dynamics Problems, centered around an example of using coordinate free numerics,Machine and Collection Abstractions for User-Implemented Data-Parallel Programming, exploiting the higher abstraction level when parallelising code, andAn Algebraic Programming Style for Numerical Software and its Optimization, looking at high-level transformations enabled by the domain specific programming style.

The rational numbers as an abstract data type

“…The problem is connected to many others such as the algebraic approaches to numerical software for scientific simulation, in Haveraaen [2000] and Haveraaen et al [2005], and to 3D and 4D volume graphics, in Chen and Tucker [2000]. In fact, it is not an uncommon view that the problem of integrating discrete and continuous computation is a barrier to progress in computer science and its application.…”

Coordinate-free numerics: all your variation points for free?

“…The topic coordinate-free numerics [MKH96,Bjø00] was developed from the motivation of simplifying tensor calculus notation. This initiated a broader investigation of the PDE domain concepts using a methodology from algebraic specifications [Hav00a]. The result was a radical redesign of the PDE domain structure.…”

Axiom-based testing for C++

“…First the concepts need to be developed. This will be an unfamiliar activity for most system developers, but we have already shown [8] that doing this may have a profound, positive effect on software development. Then concept maps need to be written for all classes that model the concepts.…”