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Matem. Mod., 2015, Volume 27, Number 8, Pages 13–31 (Mi mm3635)  

This article is cited in 9 scientific papers (total in 9 papers)

The Lebesgues averaging method veryfication

A. V. Shilkova, M. N. Gerthevb

a Keldysh Institute of Applied Mathematics RAS, Moscow
b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region

Abstract: The work is dedicated to the research of the accuracy of the Lebesgue Averaging Method (LAM) for computing spectra of resonance radiation in solving kinetic radiation transfer equation. The method is verified for the thermal radiation transfer problem in the Earth's atmosphere. The comparison of results obtained in accordance of two variants of the LAM with the results of the precise "line-by-line" calculation has been carried out. At first variant of LAM the pure Lebesque integral is implemented at which the value of the absorption coefficient is taken as independent variable. At second variant of LAM the integral of Lebesque–Stieltjes is used with independent variable reduced to measure of Lebesques set. In order to assure purity of the experiment all the computations were performed using unique method of space-angle discretization of the kinetic equation. The high accuracy of the second variant of LAM (within 5%) has been shown with a significant cut in number of arithmetic operations in need (approximately $10^3$$10^4$ times).

Keywords: computational physics, kinetic equation of radiative transfer, line-by-line computation, Lebesgue method for averaging radiation spectra.

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English version:
Mathematical Models and Computer Simulations, 2016, 8:2, 93–107

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Document Type: Article
Received: 30.03.2015

Citation: A. V. Shilkov, M. N. Gerthev, “The Lebesgues averaging method veryfication”, Matem. Mod., 27:8 (2015), 13–31; Math. Models Comput. Simul., 8:2 (2016), 93–107

Citation in format AMSBIB
\by A.~V.~Shilkov, M.~N.~Gerthev
\paper The Lebesgues averaging method veryfication
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 8
\pages 13--31
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 2
\pages 93--107

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    This publication is cited in the following articles:
    1. A. V. Shilkov, “Uravneniya dlya spektralnykh momentov funktsii raspredeleniya fotonov”, Preprinty IPM im. M. V. Keldysha, 2015, 077, 36 pp.  mathnet
    2. M. N. Gertsev, “Vosstanovlenie sechenii molekulyarnogo pogloscheniya izlucheniya iz bazy dannykh HITRAN”, Preprinty IPM im. M. V. Keldysha, 2016, 019, 22 pp.  mathnet
    3. M. N. Gertsev, A. V. Shilkov, “Podgotovka opticheskikh konstant dlya potochechnykh i lebegovskikh raschetov atmosfernoi radiatsii”, Preprinty IPM im. M. V. Keldysha, 2016, 031, 24 pp.  mathnet
    4. A. V. Shilkov, “Metod spektralnykh momentov v modelirovanii izluchayuschei stolknovitelnoi plazmy”, Preprinty IPM im. M. V. Keldysha, 2016, 036, 48 pp.  mathnet
    5. A. V. Shilkov, “The moment method of Lebesgue aggregation and spectrum recovery in particle transport problems”, Math. Models Comput. Simul., 9:3 (2017), 263–280  mathnet  crossref  elib
    6. E. N. Aristova, M. N. Gertsev, A. V. Shilkov, “Lebesgue averaging method in serial computations of atmospheric radiation”, Comput. Math. Math. Phys., 57:6 (2017), 1022–1035  mathnet  crossref  crossref  mathscinet  isi  elib
    7. B. N. Chetverushkin, I. V. Mingalev, K. G. Orlov, V. M. Chechetkin, V. S. Mingalev, O. V. Mingalev, “Gasdynamic general circulation model of the lower and middle atmosphere of the Earth”, Math. Models Comput. Simul., 10:2 (2018), 176–185  mathnet  crossref  elib
    8. E. N. Aristova, G. O. Astafurov, A. V. Shilkov, “Raschet izlucheniya v udarnom sloe spuskaemogo kosmicheskogo apparata s uchetom detalei spektra fotonov”, Kompyuternye issledovaniya i modelirovanie, 9:4 (2017), 579–594  mathnet  crossref
    9. A. V. Shilkov, N. A. Sivakov, “Modelirovanie perenosa tepla izlucheniem v dvizhuscheisya plazme s uchetom doplerovskogo sdviga linii”, Preprinty IPM im. M. V. Keldysha, 2018, 250, 30 pp.  mathnet  crossref
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