Forschungsberichte Des Fachbereichs Informatik Deriving Parallel Numerical Algorithms Using Data Distribution Algebras: Wang's Algorithm Deriving Parallel Numerical Algorithms Using Data Distribution Algebras: Wang's Algorithm

Parallel and distributed programming are much more diicult than the development of sequential algorithms due to data distribution issues and communication requirements. This paper presents a methodology that enables the 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 speciic parallel implementations. Communication is speciied implicitly through the access to overlapping parts of covers. Such speciications enable the derivation of explicit lower-level communication statements. We illustrate the concepts by a complete derivation of Wang's partition algorithm for the solution of tridiagonal systems of linear equations.