Finite element investigation of a void region on light propagation in scattering media using the radiative transfer equation

2019 ◽  
Author(s):  
Kosuke Tabayashi ◽  
Hiroyuki Fujii ◽  
Kazumichi Kobayashi ◽  
Masao Watanabe
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Light Propagation ◽  
Radiative Transfer Equation ◽  
Scattering Media

A New Stabilized Finite Element Formulation for Solving Radiative Transfer Equation

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
L. Zhang ◽  
J. M. Zhao ◽  
L. H. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Stabilized Finite Element ◽  
Element Method

A new stabilized finite element formulation for solving radiative transfer equation is presented. It owns the salient feature of least-squares finite element method (LSFEM), i.e., free of the tuning parameter that appears in the streamline upwind/Petrov–Galerkin (SUPG) finite element method. The new finite element formulation is based on a second-order form of the radiative transfer equation. The second-order term will provide essential diffusion as the artificial diffusion introduced in traditional stabilized schemes to ensure stability. The performance of the new method was evaluated using challenging test cases featuring strong medium inhomogeneity and large gradient of radiative intensity field. It is demonstrated to be computationally efficient and capable of solving radiative heat transfer in strongly inhomogeneous media with even better accuracy than the LSFEM, and hence a promising alternative finite element formulation for solving complex radiative transfer problems.

Finite element approximations for the radiative transfer equation

2006 ◽  
Author(s):  
Marko Vauhkonen ◽  
Tanja Tarvainen ◽  
Ville Kolehmainen ◽  
Jari P. Kaipio
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Finite Element Approximations
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