Far Eastern Mathematical Journal

To content of the issue


On selecting free path length sampling method for solving the non-stationary radiation transport equation using graphic accelerators


Donskaya M.A., Yarovenko I.P.

2024, issue 1, P. 33-44
DOI: https://doi.org/10.47910/FEMJ202404


Abstract
The paper considers the issues of mathematical modeling of the non-stationary transfer of X-ray radiation. We describe the process using an initial-boundary problem for the radiation transfer equation, which is solved by the weighted Monte Carlo method. The implementation of the method proposed using parallel calculations on graphic processor units (GPU) is discussed.

Keywords:
radiative transfer equation, maximum crossection method, Monte Carlo methods, parallel computing.

Download the article (PDF-file)

References

[1] Bal G., “Inverse transport theory and applications”, Inverse Problems, 25:5, (2009), 025019.
[2] Prokhorov I.V., Sushchenko A.A., “Issledovanie zadachi akusticheskogo zondirovaniia morskogo dna metodami teorii perenosa izlucheniia”, Akusticheskii zhurnal, 61:3, (2015), 400–408.
[3] Anikonov D.S., Kovtaniuk A.E., Prokhorov I.V., Ispol'zovanie uravneniia perenosa v tomografii, Logos, M., 2000.
[4] Fano U., Spenser L., Perenos gamma izlucheniia, Gosatomizdat, M., 1963.
[5] Cherchin'iani K., Teoriia i prilozheniia uravneniia Bol'tsmana, Mir, M., 1978.
[6] Budak V.P., Savenkov V.I., “O novom reshenii uravneniia perenosa izlucheniia v ramkakh malouglovogo priblizheniia”, Tp. Mosk. energ. in-t, Vyp. 591, (1982), 141–144.
[7] Strelkov S.A., Sushkevich T.A., Preprinty IPM im. M.V. Keldysha 65, 1988.
[8] Radiatsionnyi perenos v rasseivaiushchei i pogloshchaiushchei atmosferakh: standartnye vychislitel'nye protsedury, red. Zh. Lenobl', Deepak Publishing, 1990.
[9] Iamshchikov V.M., “Analiticheskoe reshenie zadachi o perenose nemonokhromaticheskogo napravlennogo izlucheniia v rezonansno pogloshchaiushchei srede”, Optika i spektroskopiia, 131:5, 705–710.
[10] Marchuk G.I., Mikhailov G.A., Nazaraliev M.A., Metod Monte-Karlo v atmosfernoi optike, Nauka, Novosibirsk, 1976.
[11] Sobol' I.M., Chislennye metody Monte-Karlo, Nauka, Moskva, 1973.
[12] Mikhailov G.A., Medvedev I.N., Optimizatsiia vesovykh algoritmov statisticheskogo modelirovaniia, Omega Print, Novosibirsk, 2011.
[13] Boreskov A.V., Kharlamov A.A., Osnovy raboty s tekhnologiei CUDA, DMK Press, M., 2010.
[14] Zhukovskii M.E., Uskov R.V., “Modelirovanie vzaimodeistviia gamma-izlucheniia s veshchestvom na gibridnykh vychislitel'nykh sistemakh”, Matematicheskoe modelirovanie, 23:7, (2011), 20-32.
[15] Alerstam E., Svensson T., Andersson-Engels S., “Parallel Computing with Graphics Processing Units for High-Speed Monte Carlo Simulation of Photon Migration”, Journal of biomedical optics., 13:6, (2008), 060504.
[16] Uskov R.V., “O nekotorykh osobennostiakh primeneniia tekhnologii CUDA dlia modelirovaniia perenosa izlucheniia”, Vestnik Moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. Seriia «Estestvennye nauki», 2011, № 3, 71–83.
[17] MC GPU project, Monte Carlo simulation of x-ray transport in a GPU with CUDA, http://code.google.com/p/mcgpu/.
[18] Periyasamy V., Pramanik M., “Advances in Monte Carlo Simulation for Light Propagation in Tissue”, IEEE Reviews in Biomedical Engineering, 2017, 1–11.
[19] Russkova T., “Monte Carlo Simulation of the Solar Radiation Transfer in a Cloudy Atmosphere with the Use of Graphic Processor and NVIDIA CUDA Technology”, Atmospheric and Oceanic Optics, 31, (2018), 119–130.
[20] Chetverushkin B.N., Markov M.B., Uskov R.V., “O rasparallelivanii metoda chastits dlia gibridnogo superkomp'iutera”, Doklady Rossiiskoi akademii nauk. Matematika, informatika, protsessy upravleniia, 2022, № 505, 19–23.
[21] Fetisov, “X-ray diffraction methods for structural diagnostics of materials: progress and achievements”, Physics-Uspekhi, 63:1, (2020), 2–32.
[22] Kuznetsov V.S., Nikolaeva O.V., Bass L.P., Bykov A.V., “Modelirovanie rasprostraneniia ul'trakorotkogo impul'sa sveta cherez sil'no rasseivaiushchuiu sredu”, Matematicheskoe modelirovanie, 21:4, (2009), 3–14.
[23] Prokhorov I.V., Yarovenko I.P., “Determination of the attenuation coefficient for the nonstationary radiative transfer equation”, Comput. Math. Math. Phys., 61:12, (2021), 2088–2101.
[24] Yarovenko I.P., Kazantsev I.G., “An extrapolation method for improving the linearity of CT-values in X-ray pulsed tomography”, Dal'nevost. matem. zhurn., 22:2, (2022), 269–275.
[25] Coleman W.A., “Mathematical verification of a certain Monte Carlo sampling technique to radiation transport problems”, Nucl. Sci. Eng., 32:1, (1968), 76–81.
[26] Mikhailov G.A., Averina T.A., “Algoritm maksimal'nogo secheniia v metode Monte- Karlo”, Doklady Akademii nauk, 428:2, (2009), 163–165.
[27] Antiufeev V.S., “K obosnovaniiu modifikatsii metoda maksimal'nogo secheniia”, Vychislitel'nye tekhnologii, 17:2, (2012), 13–19.
[28] Prokhorov I.V., Zhuplev A.S., “Ob effektivnosti metodov maksimal'nogo secheniia v teorii perenosa izlucheniia”, Komp'iuternye issledovaniia i modelirovanie, 5:4, (2013), 573–582.

To content of the issue