Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements

2016 ◽  
Vol 179 ◽  
pp. 149-164 ◽  
Author(s):  
D. Le Hardy ◽  
Y. Favennec ◽  
B. Rousseau
Keyword(s):  
Steady State ◽  
Finite Elements ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Participating Media ◽  
Specular Reflections

Propagation of Ultra-Short-Pulse Radiation in Participating Media: A Laguerre-Galerkin Solution

2007 ◽  
Author(s):  
Tuba Okutucu ◽  
Yaman Yener
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Transfer Problem ◽  
Short Pulse ◽  
Optical Tomography ◽  
Time Derivative ◽  
Product Analysis ◽  
Participating Media ◽  
Radiative Transfer Problem

Transient analysis of the radiative transfer problem in participating media has become essential due to the recent applications involving extremely small time scales. In classical radiation problems, the time derivative term in the radiative transfer equation has a negligible order of magnitude compared to the others. Lasers of pico- to femtosecond pulse durations are now being used to investigate the properties of scattering and absorbing media in such applications as, optical tomography, combustion product analysis, and remote sensing. For such applications, the time derivative in the radiative transfer equation can no longer be neglected. Numerous approaches such as, integral formulation, direct numerical approach, discrete ordinates method, Monte Carlo simulations, and Galerkin technique have been introduced for the solution of transient radiative transfer problems in participating media. In the present work, Laguerre-Galerkin solutions for both rectangular and Gaussian incident pulse profiles are presented.

Vectorial finite elements for solving the radiative transfer equation

2018 ◽  
Vol 212 ◽  
pp. 59-74 ◽  
Author(s):  
M.A. Badri ◽  
P. Jolivet ◽  
B. Rousseau ◽  
S. Le Corre ◽  
H. Digonnet ◽  
...  
Keyword(s):  
Finite Elements ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Vol 132 (2) ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Finite Elements ◽  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For nonscattering radiative transfer, sparse finite elements [2007, “Sparse Finite Elements for Non-Scattering Radiative Transfer in Diffuse Regimes,” ICHMT Fifth International Symposium of Radiative Transfer, Bodrum, Turkey; 2008, “Sparse Adaptive Finite Elements for Radiative Transfer,” J. Comput. Phys., 227(12), pp. 6071–6105] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared with the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

A Finite-Difference-Method Solution to Two-dimensional Steady-State Radiative Transfer Equation

2010 ◽  
Vol 39 (9) ◽  
pp. 1594-1601
Author(s):  
金蒙 JIN Meng ◽  
高峰 GAO Feng ◽  
李娇 LI Jiao ◽  
赵会娟 ZHAO Hui-juan
Keyword(s):  
Steady State ◽  
Radiative Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Two Dimensional
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