辐射传输方程的三阶球谐展开(P_3)近似的有限元法求解  

Finite Element Method for Three-Order(P_3) Approximation of Radiative Transfer Equation

作　　者：马文娟[1] 高峰[1] 朱苹苹[1] 易茜[1] 

机构地区：[1]天津大学精密仪器与光电子工程学院,天津300072

出　　处：《光子学报》2011年第7期1117-1121,共5页Acta Photonica Sinica

基　　金：国家自然科学基金(No.30870657;No.30970775);国家高技术研究发展计划(No.2009AA02Z413);天津市自然科学基金(No.09JCZDJC18200;No.10JCZDJC17300)资助

摘　　要：从辐射传输方程出发,应用球谐函数方法对辐射率进行多项式展开,并利用球谐函数的正交性和递推性,在二维笛卡儿坐标下,导出了三阶展开的球谐函数微分方程组(P3近似),改进了以往成像文献中忽略各项异性因子的P3近似,并用有限元方法对二维圆域均匀和非均匀两种情况做了数值模拟.与漫射近似模型相比较,P3近似能更准确地描述光源附近及吸收较强情况下边界的光辐射分布情况.The flux takes the form of an expansion in spherical harmonics,and the two-dimensional spherical harmonics equations to three-order for anisotropic scattering is drived.The equations is solved using finite element method and compared the solutions with the first-order diffusion equation and Monte Carlo simulation.The resolut shows that the developed three-order model with high absorb coefficient is able to significantly improve the diffusion solution in circle geometry,and the radiance distribution close to light source is more accurate.

关 键 词：辐射传输方程 球谐函数 扩散方程 有限元方法 蒙特卡洛模拟 

分 类 号：Q63[生物学—生物物理学]