Deriving parallel numerical algorithms using data distribution algebras: Wang´s algorithm

Parallel and distributed programming are much more difficult than the development of sequential algorithms because of data distribution issues and communication requirements. The paper presents a methodology that enables an abstract description of the distribution of data structures by means of overlapping covers that form data distribution algebras. Algorithms are formulated and derived by transformation in a functional environment using skeletons, i.e. higher order functions with specific parallel implementations. Communication is specified implicitly through the access to overlapping parts of covers. Such specifications enable the derivation of explicit lower level communication statements. We illustrate the concepts by a complete derivation of H.H. Wang´s (1981) partition algorithm for the solution of tridiagonal systems of linear equations