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Computational Forward and Inverse Radiative Transfer

计算正向和反向辐射传输

基本信息

批准号：
2012860
负责人：
Hong-Kai Zhao
金额：
$ 25万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012860&HistoricalAwards=false
关键词：
Computational Forward Inverse Radiative Transfer

项目摘要

The radiative transfer equation (RTE) is an important modeling tool with applications in biomedical imaging, clinical radiation therapy treatment planning, study of the composition and structure of atmosphere, and other fields. Because of its complicated structure, the RTE presents challenges to analysis and simulation. This research project aims at developing novel, accurate, and eﬃcient computational methods for both forward and inverse radiative transfer problems. More generally, the insights obtained in this project are expected to provide new perspectives on solving a class of integral equations. The mathematical tools and computational algorithms under development will be disseminated broadly for advancing scientiﬁc and technological progress. Integration of research with education at diﬀerent levels will provide training for computational mathematicians. Supervised research projects and seminars related to the proposed research will be available to junior/senior undergraduates and graduate students. Participation of members of underrepresented groups will be encouraged.Solutions to radiative transfer equations behave very diﬀerently in diﬀerent regions/regimes. These challenges require well-designed and well-understood numerical algorithms that can take into account special properties and structures of the RTE and its solution associated with the underlying application. Although studies and developments of numerical methods for RTE based on diﬀerential and probabilistic formulations have been done, integral-formulation-based approaches are less understood and not fully developed. This project will systematically develop and analyze eﬃcient numerical algorithms based on integral formulation and also explore a combination of integral and diﬀerential formulations. The key idea is to utilize dimension reduction, careful treatment of singularity, and the special structures of the resulting dense matrix to develop fast solvers. This research is applicable to numerical simulation of radiation hydrodynamics and modeling of wave propagation in random media.Further applications in inverse problems that are modeled by RTE, such as optical tomography, photoacoustic tomography, ﬂuorescence imaging, etc., will be studied as well.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

辐射传递方程（RTE）是一种重要的建模工具，在生物医学成像、临床放射治疗计划、大气成分和结构研究等领域都有应用。由于RTE结构复杂，给分析和仿真带来了挑战。本研究项目旨在为正、逆辐射传输问题开发新颖、准确、高效的计算方法。更一般地说，在这个项目中获得的见解有望为解决一类积分方程提供新的视角。广泛推广正在开发的数学工具和计算算法，促进科学技术进步。将研究与不同层次的教育相结合将为计算数学家提供培训。指导下的研究项目和与拟议研究相关的研讨会将提供给大三/大四本科生和研究生。将鼓励代表性不足群体的成员参加。辐射传递方程的解在不同的区域/状态下表现得非常不同。这些挑战需要精心设计和易于理解的数值算法，这些算法可以考虑到RTE的特殊属性和结构以及与底层应用程序相关的解决方案。尽管基于微分和概率公式的RTE数值方法的研究和发展已经完成，但基于积分公式的方法却很少被理解，也没有得到充分的发展。该项目将系统地开发和分析基于积分公式的高效数值算法，并探索积分和微分公式的结合。关键思想是利用降维，仔细处理奇点，以及所得到的密集矩阵的特殊结构来开发快速求解器。本研究可应用于辐射流体力学数值模拟和随机介质中波传播的模拟。此外，还将研究RTE在光学层析成像、光声层析成像、荧光成像等反问题中的进一步应用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。