Metaprogramming for the Creation of Scientific Software

A major cost in scientific computing is the creation of software that performs the numerical compu-tations. This paper presents preliminary results on research to build a framework for automat-ing the construction of numerical solvers for dif-ferential equations. Within this framework, the scientific computing problem is described using a very high level programming language that cap-tures the original differential equations in a nat-ural fashion. A sequence of code "transform-ers " are used to gradually refine the high level description of the problem into a concrete, exe-cutable form. Numerical techniques like the fi-nite element method, the spectral method and the Crank-Nicolson discretization scheme are encoded in these transformers and once so encoded can be applied to a wide variety of different problems