Large scale scientific computing necessitates finding a way to match the high level understanding of how a problem can be solved with the details of its computation in a processing environment organized as networks of processors. Effective utilization of parallel architectures can then be achieved by using formal methods to describe both computations and computational organizations within these networks. By returning to the mathematical treatment of a problem as a high level numerical algorithm we can express it as an algorithmic formalism that captures the inherent parallelism of the computation. We then give a meta description of an architecture followed by the use of transformational techniques to convert the high level description into a program that utilizes the architecture effectively. The hope is that one formalism can be used to describe both computations as well as architectures and that a methodology for automatically transforming computations can be developed. The formalism and methodology presented in the paper is a first step toward the ambitious goals described above. It uses a theory of arrays, the Psi calculus, as the formalism, and two levels of conversions—one for simplification and another for data mapping.