辐射传输方程的变分和Galerkin离散格式  

VARIATIONAL FORMULATION AND GALERKIN DISCRETIZATION SCHEMES FOR RADIATIVE TRANSFER EQUATION

作　　者：何莉敏[1,2] 王娟 侯玉双[1,3] He Limin;Wang Juan;Hou Yushuang(School of Science,Inner Mongolia University of Science and Technology,Baotou 014010;School of Mathematics and Statistics,Xi＇an Jiaotong University,Xi＇an,71004)

机构地区：[1]内蒙古科技大学理学院,包头014010 [2]西安交通大学数学与统计学院,西安710049 [3]西南大学物理科学与技术学院,重庆400715

出　　处：《高等学校计算数学学报》2018年第3期275-288,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目(61663035)和内蒙古自然科学基金项目(2015BS0604,2018MS06017).

摘　　要：辐射传输方程（radiative transfer equation：RTE）有着非常广泛的应用，例如天体物理[1]，大气和海洋[2，3]，辐射传热[4]，中子输运[5，6]，光分子成像[7,8]等等．辐射传输方程是光学分子成像的正向问题，从物理角度而言可归结为光子在生物组织中的传输问题，然而辐射传输方程是一个偏微分方程，本质上是一个积分．微分的双曲型问题.The radiative transfer equation（RTE） arises in a wide variety of applications in sciences and engineering. In this paper, based on four forms of RTE in biomedical imaging, a operator framework for RTE under the non-homogeneous boundary conditions is proposed. Their variational formulations and variational principle are derived, respectively. Energy estimates and exponential stability for variational problem are discussed, at the same time, Galerkin semi-discretization problem with unsteady symmetry RTE is analysized and error estimate is shown. Numerical analysis theory foundation is provided for the purpose of further studying RTE.

关 键 词：辐射传输方程 GALERKIN 离散格式 偏微分方程 变分 天体物理 分子成像 双曲型问题 

分 类 号：O241.8[理学—计算数学]