Chain Models and Finite Element Analysis :

Algebraic-topological k-chains deened over nite cell complexes have been proposed as a uniform computational means of representing physical objects, systems and properties. This article introduces Chains, a computer language whose basic datatypes are cells, cell complexes, and k-chains. To illustrate how Chains may be used in numerical computing, we develop a two page Chains program that completely speciies a nite element solution to plane strain, including symbolic deenition of quadratic shape functions, the related \element stiiness matrices," and an algebraic-topological speciication of the assembly process. In contrast to a textbook derivation of the nite element method (which it closely resembles), this program is a fully formal nite element computation, and hence is a step towards the goal of improving the process of creating software for scientiic computing by raising the semantic level at which physical systems are speciied.