Functional Programming for Finite Element Analysis

This report is a detailed study of the application of functional programming to a typical problem in engineering computing---finite element structural analysis. The report assumes no prior knowledge of structural analysis, but does presume some familiarity with the Miranda programming language. It begins by showing how a basic linear algebra (BLAS) library can be built in Miranda, to perform elementary operations on vectors and matrices of various kinds. This is then applied to the construction of a simple finite element analysis package. Performance results under various functional language implementations are presented, and several different formulations of the central computations are investigated. Finally opportunities for parallel computation are identified. 1 Introduction This paper studies the application of functional programming in a fairly realistic and extended case study. We explore some of the claims, strengths and weaknesses of the functional approach, in terms of clarit..