U.S.-Western Europe Regional Cooperative Research: NumericalMethods in Particle Transport Theory

该奖项支持北卡罗来纳州立大学的Charles Siewert博士与阿姆斯特丹自由大学的J. Hovenier博士、博洛尼亚大学的V. Boffi博士和Boffi博士在应用数学领域的合作。里尔大学的C. Devaux和Y. Fouquart说。他们利用粒子输运理论中的解析和计算方法，研究辐射传递一般领域中的两个基本问题：探照灯问题和一般偏振问题。在这两种情况下，最初由siwert博士在中子输运理论的背景下导出的F-N方法将成为数值研究的基础。研究辐射传输中的经典探照灯问题，作为构建一类多维传输问题高精度数值解的第一次尝试。此外，需要使用精确的分析和高度精确的数值方法来构建和实现包括极化效应在内的辐射传输模型中基本问题的计算可行的解决方案。本文将采用包含极化效应的一般辐射能量传递模型来研究输运理论中的矢量问题，以解决非方位对称问题的计算困难。西沃特博士在线性运输理论方面有着杰出的贡献，在富有成效的国际合作方面有着悠久的历史。与他合作的三个国外研究小组是辐射传输和数值输运理论的主要研究中心，为分享新的数据和数值结果奠定了良好的基础。探照灯问题和多次散射辐射的偏振问题是钱德拉塞卡在四十多年前首先提出的两个重要问题。它们在数值分析方法方面尤其具有挑战性。鉴于他们过去的工作和日益增强的计算机能力，预计西沃特博士将继续与他的欧洲同事合作，为建立辐射传输理论中这些具有挑战性的问题的明确解决方案做出重大贡献。此外，他们在偏振问题上的工作结果可以提供一个有用的诊断工具，从观测到的强度和偏振曲线推断物理性质。

This award supports Dr. Charles Siewert of North Carolina State University to collaborate in applied mathematics with Dr. J. Hovenier of the Free University of Amsterdam, Dr. V. Boffi of the University of Bologna, and Drs. C. Devaux and Y. Fouquart of the University of Lille. Using analytical and computational methods in particle transport theory, they are working on two basic problems in the general field of radiative transfer: the searchlight problem and the general polarization problem. In both cases, the F-N method, derived originally by Dr. Siewert in the context of neutron transport theory, is to be the basis of the numerical studies. The classical searchlight problem in radiative transfer will be studied as a first attempt to construct highly accurate numerical solutions to a class of multi-dimensional transport problems. In addition, exact analysis and highly accurate numerical methods are to be used to construct and implement computationally viable solutions to basic problems in radiative transfer models that include polarization effects. A general radiant energy transfer model that includes polarization effects will be used to study vector problems in transport theory where the computational difficulties encountered for non-azimuthally symmetric problems must be resolved. Dr. Siewert has a distinguished record of contributions to linear transport theory and a long history of productive international collaboration. The three foreign groups with which he is collaborating are major centers of research in radiative transfer and numerical transport theory and a basis for sharing new data and numerical results has been well established. The searchlight problem and polarization for multiply scattered radiation are two important problems first proposed over forty years ago by Chandrasekhar. They are particularly challenging in terms of numerical analysis methods. In light of their past work and the increasing power of computers, it is anticipated that Dr. Siewert's continued collaboration with his European colleagues will contribute significantly to the establishment of definitive solutions to these challenging problems in radiative transfer theory. In addition, the results of their work on the polarization problem may offer a useful diagnostic tool in inferring physical properties from observed intensity and polarization profiles.