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Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations

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Języki publikacji
EN
Abstrakty
EN
Various numerical methods were proposed for analysis of the light scattering phenomenon. An important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation. Discrete dipole approximation uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo algorithm as one of them was proposed. In this research, we analyze the application of the Monte Carlo algorithm for two cases: the light scattering by large particles and by random conglomerates of small particles. We show that if proper preconditioning of the numerical problem is applied, the Monte Carlo algorithm can solve the underlying systems of linear equations. We also show that the efficiency of the Monte Carlo algorithm can be increased by reusing performed computations for various incident electromagnetic waves and the applicability of the Monte Carlo algorithm depends on the particular use case. It is unlikely to be used in the case of light scattering by the large particles due to computational times inferior comparing with the other numerical methods but may become useful in the case of light scattering by the random conglomerates of small scattering particles.
Czasopismo
Rocznik
Strony
1--15
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
  • Department of Metrology and Optoelectronics, Faculty of Electronics, Telecommunications and Engineering, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
  • Department of Metrology and Optoelectronics, Faculty of Electronics, Telecommunications and Engineering, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
Bibliografia
  • [1] YURKIN M.A., HOEKSTRA A.G., The discrete dipole approximation: an overview and recent developments, Journal of Quantitative Spectroscopy and Radiative Transfer 106(1–3), 2007, pp. 558–589,DOI:10.1016/j.jqsrt.2007.01.034.
  • [2] MISHCHENKO M.I., Electromagnetic Scattering by Particles and Particle Groups: An Introduction,Cambridge University Press, Cambridge, 2014.
  • [3] DRAINE B.T., FLATAU P.J., Discrete-dipole approximation for scattering calculations, Journal of the Optical Society of America A 11(4), 1994, pp. 1491–1499, DOI:10.1364/JOSAA.11.001491.
  • [4] MISCHCHENKO M.I., TRAVIS L.D., MACKOWSKI D.W., T-matrix computations of light scattering bynonspherical particles: a review, Journal of Quantitative Spectroscopy and Radiative Transfer 55(5),1996, pp. 535–575, DOI:10.1016/0022-4073(96)00002-7.
  • [5] MACKOWSKI D.W., MISHCHENKO M.I., A multiple sphere T-matrix Fortran code for use on parallel computer clusters, Journal of Quantitative Spectroscopy and Radiative Transfer 112(13), 2011, pp. 2182–2192, DOI:10.1016/j.jqsrt.2011.02.019.
  • [6] MARTELLI G.Z.F., DEL BAINCO S., ISMAELLI A., Light Propagation Through Biological Tissue and Other Diffusive Media: Theory, Solutions and Software, SPIE Press Monograph, Vol. PM193, Bellingham, 2010.
  • [7] WANG L., JACQUES S.L., ZHENG L., MCML – Monte Carlo modeling of light transport in multi-layeredtissues, Computer Methods and Programs in Biomedicine 47(2), 1995, pp. 131–146, DOI:10.1016/0169-2607(95)01640-F.
  • [8] JIN J-M., The Finite Element Method in Electromagnetics, 3rd Ed., Wiley, New York, 2014.
  • [9] TAFLOVE A., HAGNESS S.C., Computational Electrodynamics: The Finite-Difference Time-DomainMethod, 3rd Ed., Artech House, Norwood, MA, 2005.
  • [10] VANDE HULST H.C., Light Scattering by Small Particles, Dover Publications, New York, 1981.
  • [11] DEVANEY A.J., Mathematical Foundations of Imaging, Tomography and Wavefield Inversion, Cambridge University Press, Cambridge, 2012.
  • [12] GOODMAN J.J., DRAINE B.T., FLATAU P.J., Application of fast-Fourier-transform techniques to the discrete-dipole approximation, Optics Letters 16(15), 1991, pp. 1198–1200, DOI:10.1364/OL.16.001198.
  • [13] DUNN W.L., SHULTIS J.K., Exploring Monte Carlo Methods, Elsevier Science, Amsterdam, 2011.
  • [14] DOUCET A., JOHANSEN A.M., TADIĆ V.B., On solving integral equations using Markov chain Monte Carlo methods, Applied Mathematics and Computation 216(10), 2010, pp. 2869–2880, DOI:10.1016/j.amc.2010.03.138.
  • [15] JI H., MASCAGNI M., LI Y., Convergence analysis of Markov chain Monte Carlo linear solvers using Ulam–von Neumann algorithm, Computer Science Faculty Publications 51(4), 2013, pp. 2107–2122, DOI:10.1137/130904867.
  • [16] SRINIVASAN A., Monte Carlo linear solvers with non-diagonal splitting, Mathematics and Computers in Simulation 80(6), 2010, pp. 1133–1143, DOI:10.1016/j.matcom.2009.03.010.
  • [17] PEREIRA P.F., SHERIF S.S., Simulation of the interaction of light and tissue in a large volume usinga Markov chain Monte Carlo method, Proceedings of SPIE 8412, 2012, article 841218, DOI:10.1117/12.2001455.
  • [18] KRASZEWSKI M., PLUCIŃSKI J., Coherent-wave Monte Carlo method for simulating light propagationin tissue, Proceedings of SPIE 9706, 2016, article 970611, DOI:10.1117/12.2213213.
  • [19] LAKHTAKIA A., Strong and weak forms of the method of moments and the coupled dipole method forscattering of time-harmonic electromagnetic fields, International Journal of Modern Physics C 3(3),1992, pp. 583–603, DOI:10.1142/S0129183192000385.
  • [20] SAAD Y., Iterative methods for sparse linear systems, 2nd Ed., Society for Industrial and Applied Mathematics, Philadelphia, 2003.
  • [21] LOKE V.L.Y., MENGÜÇ M.P., NIEMINEM T.A., Discrete-dipole approximation with surface interaction:computational toolbox for MATLAB, Journal of Quantitative Spectroscopy and Radiative Transfer 112(11), 2011, pp. 1711–1725, DOI:10.1016/j.jqsrt.2011.03.012.
  • [22] SKORUPSKI K., Using the DDA (discrete dipole approximation) method in determining the extinction cross section of black carbon, Metrology and Measurement Systems 22(1), 2015, pp. 153–164, DOI:10.1515/mms-2015-0013.
  • [23] VAN ROSSUM M.C.W., NIEUWENHUIZEN TH.M., Multiple scattering of classical waves: microscopy, mesoscopy and diffusion, Reviews of Modern Physics 71(1), 1999, pp. 313–371, DOI:10.1103/RevModPhys.71.313.
  • [24] DORONIN A., RADOSEVICH A.J., BACKMAN V., MEGLINSKI I., Two electric field Monte Carlo modelsof coherent backscattering of polarized light, Journal of the Optical Society of America A 31(11),2014, pp. 2394–2400, DOI:10.1364/JOSAA.31.002394.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9e8eeb6c-0a10-4eb6-aa97-fcede9014609
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