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

在工程分析中，通常必须作出折衷，即使用近似值，因为完整或完整的问题不适合进行严格的数学分析。然而，随着当前计算能力的爆炸性增长，这些公式中的许多都可以从数值解的角度进行显著改进，而不是寻求近似的解析解。一个很好的例子是输运方程的建立和求解，它在遥感、通信、计算机图像表示和辐射热传输等各种应用中都存在。基于多重散射理论，推导了波在含有随机分布的非均匀背景离散散射体的半有界随机介质中的一般传输方程。计算技术将被用来解决这个多重散射问题。此外，还将与现有的极限近似解(例如扭曲Born近似和经典传递方程)进行比较。这项研究将由来自不同工程、机械和土木工程领域的两名教员在一所本科机构进行，他们利用NSF超级计算机中心的超级计算机资源。这种有限的短期支持将有助于激发更多的创造性环境，为跨学科的工程研究探索新的计算方法。

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.