A Deficiency Problem of the Least Squares Finite ElementMethod for Solving Radiative Transfer in Strongly I nhomogeneous Media J.M. Zhao (jmzhao@hit.edu.cn), J.Y. Tan (tanjy@hit.edu.cn), L.H.Liu(lhliu@hit.edu.cn) ABSTRACT : T he accuracy and stabilityof the least squares finite element method (LSFEM) and the Galerkin finiteelement method (GFEM) for solving radiative transfer in homogeneous andinhomogeneous media are studied theoretically via a frequency domain technique.The theoretical result confirms the traditional understanding of the superiorstability of the LSFEM as compared to the GFEM. However, it is demonstrated numericallyand proved theoretically that the LSFEM will suffer a deficiency problem forsolving radiative transfer in media with strong inhomogeneity . Thisdeficiency problem of the LSFEM will cause a severe accuracy degradation, whichcompromises too much of the performance of the LSFEM and makes it not a goodchoice to solve radiative transfer in strongly inhomogeneous media. It is also theoreticallyproved that the LSFEM is equivalent to a second order form of radiativetransfer equation discretized by the central difference scheme. This paper has been accepted by JQSRT. The preprint can be download here from arXiv server: http://arxiv.org/abs/1203.0615
辐射传递问题求解的谱元法/有限元法程序代码 谱元法可以看做有限元法的一种，其单元形函数的采用正交多项式构造，空间离散具有很高精度，精度阶数可以通过改变近似多项式的阶数根据需要任意调节。 有疑问或建议欢迎联系：赵军明 (jmzhao@hit.edu.cn) 。 1）均匀折射率介质内辐射传递求解的谱元法代码 代码为Matlab编写，可用于求解1维吸收、发射及各向异性散射性均匀折射率平板内的辐射换热。 算法描述参加以下文献： J.M. Zhao , L.H. Liu. Least-Squares Spectral Element Method for Radiative Heat Transfer in Semitransparent Media. Numerical Heat Transfer Part B . Nov. 2006, 50(5): 473-489. 刘林华 , 赵军明 , 谈和平 . 辐射传递方程数值模拟的有限元和谱元法 . 科学出版社 . 2008. 点此下载 2）梯度折射率介质内辐射传递求解的谱元法代码： 代码为Matlab编写，可用于求解1维吸收、发射及各向异性散射性梯度折射率平板内的辐射换热。 算法描述参加以下文献： J.M. Zhao , L.H. Liu. Solution of Radiative Heat Transfer in Graded Index Media by Least Square Spectral Element Method. International Journal of Heat and Mass Transfer . 2007, 50: 2634-2642. 刘林华 , 赵军明 , 谈和平 . 辐射传递方程数值模拟的有限元和谱元法 . 科学出版社 . 2008. 点此下载 Spectral / Finite Element Method (SEM, FEM) Code for Radiative Transfer J.M. Zhao (jmzhao@hit.edu.cn) Spectral element method (SEM) can be considered as a special kind of finite element method. In the SEM, the nodal basis functions are constructed based on orthorgonal polynomials, which ensures very high accuracy of spatial discretization and the order of accuracy can be easily selected by changing the polynomial order. This page contains the SEM source codes for solving radiative heat transfer in 1D infinite slab. These codes were implemented through program language of Matlab and are fully vectorized to best utilize the advantages of matrix language of MATLAB. Have any questions or advices, feel free to contact J.M. Zhao (jmzhao@hit.edu.cn). The codes can be downloaded here: 1) SEM code for solving radiative heat transfer in 1D slab. Algorithm of this code was discribed in the following refereces: J.M. Zhao , L.H. Liu. Least-Squares Spectral Element Method for Radiative Heat Transfer in Semitransparent Media. Numerical Heat Transfer Part B . Nov. 2006, 50(5): 473-489. J.M. Zhao , L.H. Liu. Least-Squares Spectral Element Method for Radiative Heat Transfer in Semitransparent Media. Numerical Heat Transfer Part B . 2006, 50(5): 473-489. L.H.Liu, J.M. Zhao, H.P. Tan. The finite element method and spectral element methodfor numerical simulation of radiative transfer equation . Beijing: Science press , 2008. DOWNLOAD 2) SEM code for solving radiative heat transfer in variable refractive index (graded index) 1D slab. Algorithm of this code was discribed in the following refereces: J.M. Zhao , L.H. Liu. Solution of Radiative Heat Transfer in Graded Index Media by Least Square Spectral Element Method. International Journal of Heat and Mass Transfer . 2007, 50: 2634-2642. L.H.Liu, J.M. Zhao, H.P. Tan. The finite element method and spectral element methodfor numerical simulation of radiative transfer equation . Beijing: Science press, 2008. DOWNLOAD
标签: 有限元法
