Development and comparison of different spatial numerical schemes for the radiative transfer equation resolution using three-dimensional unstructured meshes

2010 ◽  
Vol 111 (2) ◽  
pp. 264-273 ◽  
Author(s):  
R. Capdevila ◽  
C.D. Pérez-Segarra ◽  
A. Oliva
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
Numerical Schemes ◽  
Equation Resolution

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to 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 (CG) 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.

scholarly journals FIRTEZ-dz

2019 ◽  
Vol 629 ◽  
pp. A24 ◽  
Author(s):  
A. Pastor Yabar ◽  
J. M. Borrero ◽  
B. Ruiz Cobo
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Momentum Equation ◽  
Gas Pressure ◽  
Numerical Code ◽  
Physical Parameters ◽  
Geometrical Scale

We present a numerical code that solves the forward and inverse problem of the polarized radiative transfer equation in geometrical scale under the Zeeman regime. The code is fully parallelized, making it able to easily handle large observational and simulated datasets. We checked the reliability of the forward and inverse modules through different examples. In particular, we show that even when properly inferring various physical parameters (temperature, magnetic field components, and line-of-sight velocity) in optical depth, their reliability in height-scale depends on the accuracy with which the gas-pressure or density are known. The code is made publicly available as a tool to solve the radiative transfer equation and perform the inverse solution treating each pixel independently. An important feature of this code, that will be exploited in the future, is that working in geometrical-scale allows for the direct calculation of spatial derivatives, which are usually required in order to estimate the gas pressure and/or density via the momentum equation in a three-dimensional volume, in particular the three-dimensional Lorenz force.

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