A Theory of the Spatial Computational Domain

Most parallel processing methods developed for geographic analyses bind the design of domain decomposition and task scheduling to specific parallel computer architectures. These methods are not adaptable to emerging distributed computing environments that are based on Grid computing and peer-to-peer technologies. This paper presents a theory to support the development of adaptable parallel processing methods for geographic analyses performed on heterogeneous parallel processing environments. This theory of the spatial computational domain represents the computational intensity of geographic data and analysis methods, and transforms it into a common framework based on transformation theories from earlier cartographic research. The application of the theory is illustrated using an inverse distance weighted interpolation method. We describe the underpinnings of this analysis, and then address the latent parallelism of a conventional sequential algorithm based on spatial computational domain theory. Through the application of this theory, the development of domain decomposition methods is decoupled from specific high performance computer architectures and task scheduling implementations, which makes the design of generic parallel processing geographic analysis solutions feasib le