Light & Engineering 30 (5)

Volume 30
Date of publication 10/25/2022
Pages 21–30

Solution of the Radiative Transfer Equation for Vertically Inhomogeneous Media by Numerical Integration Solvers: Comparative Analysis L&E, Vol.30, No.5, 2022

Articles authors:

Ivan A. Chuprov, Daniil N. Konstantinov, Dmitry S. Efremenko, Vyacheslav V. Zemlyakov, Jiexing Gao

Ivan A. Chuprov, engineer and postgraduate student in Condensed Matter Physics at Syktyvkar State University, 2021. His main research direction: numerical simulation of physical processes

Daniil N. Konstantinov, Master in Applied Mathematics and Informatics, graduated from Moscow Institute of Physics and Technology. He is mainly engaged in Evolutionary Game Theory, Numerical Methods and Deep Learning

Dmitry S. Efremenko, Ph. D. He graduated from the Moscow Power Engineering institute (MPEI) in 2009. He received his Ph. D. degree from the Moscow State University in 2011 and the habilitation degree from MPEI in 2017. Since 2011 he works as a Research Scientist at the German Aerospace Centre (DLR). He is a docent at the Technical University of Munich. He has over 70 peer-reviewed publications. His scientific interests include radiate transfer, remote sensing, and machine learning

Vyacheslav V. Zemlyakov received his Ph. D. and Dr. Sc. degrees in Radio-physics from Southern Federal University, Rostov-on-Don, Russia, in 2005 and 2015, respectively. He is currently a Senior Researcher in Russian Research Institute, Huawei Technologies Co., Ltd., Moscow, Russia. His research interests include microwave and optical communications, with emphasis on key theory, numerical methods, and computer simulation

Jiexing Gao received the Ph. D. in Math-Phys from Lomonosov Moscow State University, Russia, in 2011. He worked at Fujian Normal University, Fuzhou, China, as an Assistant Professor. From 2014 to 2019, he was with Bell Labs, Shanghai, China, where he was engaged in research on wireless communication, localization, and robot technology. Since the end of 2019, he joined in Huawei Technologies Co., Ltd. He is currently in charge of an optical communication project. His present research interests involve optical fiber communication, math modelling of waveguides, Maxwell equations and numerical methods

Abstract:

An efficiency of the singular value decomposition (SVD) method and ordinary differential equation (ODE) solvers in finding the reflection matrix are compared. A reflection matrix can be found by solving the one-dimensional radiative transfer equation. The latter’s solution based on the discrete ordinate method leads to the singular value decomposition (SVD) method. Alternative approach consists in transforming the original problem into a matrix Riccati equation written specifically for the reflection matrix. The matrix Riccati equation is solved using numerical integration techniques for ordinary differential equations (ODEs). It is found that for a single layer case, the SVD approach is faster than the ODE solvers by an order of magnitude. Yet as the number of layers increases, the ODE solvers become more efficient than the SVD approach. In addition, they outperform the SVD method when a solution for a set of optical thicknesses of the medium should be found or when retrieval of optical thickness should be performed. The comparison between different ODE solvers is performed, as well.

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Keywords

DOI: https://doi.org/10.33383/2022-030

Article in RUS:
Svetotekhnika # 4, 2022, pp. 63–70

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