Development of a General Transfer Theory for Semi-Bounded Medium with Discrete Scatterers

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Often in engineering analysis compromises must be made, i. e. approximations are used since the full or complete problem does not lend itself to rigorous mathematical analysis. However, with the current explosive growth in computational power many of these formulations can be significantly improved with a view towards numerical solution rather than seeking an approximate analytical solution. A good example is the formulation of and the solution of the transport equation which occurs in such diverse application as remote sensing, communications, computer imagine representation, and radiative heat transfer. The General Transfer Equation will be derived based on Multiple Scattering Theory for waves propagating in a semi-bounded random medium containing randomly distributed discrete scatters with nonuniform background. Computational technique will be developed to solve this multiple scattering problem. Futhermore, comparisons will be made with existing limiting approximate solutions, e.g. Distorted Born Approximation and the classical Transfer Equation. The research will be carried out at an undergraduate institution by two faculty members from different fields of engineering; mechanical and civil engineering utilizing supercomputer resources at a NSF supercomputer center. This limited support of short duration will serve to stimulate more creative environment for cross-disciplinary engineering research to explore new computational methodologies.