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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 3, Pages 504–514 (Mi zvmmf8087)  
Functional optimization technique for numerical solution of the radiative transfer equation

O. M. Alifanov, V. V. Cherepanov

Moscow Aviation Institute, Volokolamskoe sh. 4, Moscow, 125993 Russia
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Abstract: A numerical method for solving the time-independent radiative transfer problem in a flat layer with given properties and temperature distribution is proposed. This method avoids the numerical diffusion; rather, it is based on a gradient procedure for the functional minimization of the residual of the radiative transfer integral equation. Means for suppressing computational instabilities are proposed that reduce requirements for the approximation of the operators in the optimization problem but do not change the problem objective functional.
Key words: heat transfer in a layer, integral equation, functional minimization of residual, conjugate gradient method, stabilization by restricting to the Sobolev space.
Received: 15.12.2009
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 3, Pages 467–476
DOI: https://doi.org/10.1134/S096554251103002X
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: O. M. Alifanov, V. V. Cherepanov, “Functional optimization technique for numerical solution of the radiative transfer equation”, Zh. Vychisl. Mat. Mat. Fiz., 51:3 (2011), 504–514; Comput. Math. Math. Phys., 51:3 (2011), 467–476
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:51
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