Novel Computational Approaches to the Transport Equation

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This project is directed toward computational solution of the linear particle transport equation, which usually is termed simply the ``transport equation.'' This equation historically has provided a major challenge to the state-of-the-art computer hardware available at any given time. More specifically, the project is directed toward spatial approximations to this equation, because new approaches and better basic understanding in this area seem essential to permit the solution of the transport equation in the complex material arrangements underlying some of the emerging applications of this equation (e.g., identification of underground waste locations for environmental restoration). A certain abstract model (CLOF methods) of one-dimensional approximations in particle transport is being extended and applied, as follows: a massively parallel code is being developed for a general class of one-dimensional spatial approximations; the model is being extended to multiple (two or more) spatial dimensions; a that permits computational determination of the order of accuracy of an arbitrary two-dimensional CLOF is being developed; the CLOF methods that have the very desirable property of satisfying the diffusion limit are being characterized. The corner-balance method, which is a novel spatial approximation that seems to enjoy several properties that are highly desirable for multidimensional calculations, is being extended to the three-dimensional setting, initially for parallelepiped cells, and subsequently for meshes composed of cells that are general (convex) polyhedra.