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Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles

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Title: Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles
Authors: Bi, Lei1, Yang, Ping1 pyang@tamu.edu, Kattawar, George W.2, Mishchenko, Michael I.3
Source: Journal of Quantitative Spectroscopy & Radiative Transfer. Feb2013, Vol. 116, p169-183. 15p.
Subjects: Invariant imbedding, T-matrix, Inhomogeneous materials, Boundary value problems, Integral equations, Separation of variables, Scattering (Physics), Light scattering
Abstract: Abstract: Three terms, “Waterman''s T-matrix method”, “extended boundary condition method (EBCM)”, and “null field method”, have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIM+SOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIM+SOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIM+SOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIM+SOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging. [Copyright &y& Elsevier]
Copyright of Journal of Quantitative Spectroscopy & Radiative Transfer is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Quantitative+Spectroscopy+%26+Radiative+Transfer%22">Journal of Quantitative Spectroscopy & Radiative Transfer</searchLink>. Feb2013, Vol. 116, p169-183. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Invariant+imbedding%22">Invariant imbedding</searchLink><br /><searchLink fieldCode="DE" term="%22T-matrix%22">T-matrix</searchLink><br /><searchLink fieldCode="DE" term="%22Inhomogeneous+materials%22">Inhomogeneous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+equations%22">Integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Separation+of+variables%22">Separation of variables</searchLink><br /><searchLink fieldCode="DE" term="%22Scattering+%28Physics%29%22">Scattering (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Light+scattering%22">Light scattering</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Abstract: Three terms, “Waterman''s T-matrix method”, “extended boundary condition method (EBCM)”, and “null field method”, have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIM+SOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIM+SOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIM+SOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIM+SOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of Quantitative Spectroscopy & Radiative Transfer is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jqsrt.2012.11.014
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 169
    Subjects:
      – SubjectFull: Invariant imbedding
        Type: general
      – SubjectFull: T-matrix
        Type: general
      – SubjectFull: Inhomogeneous materials
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Integral equations
        Type: general
      – SubjectFull: Separation of variables
        Type: general
      – SubjectFull: Scattering (Physics)
        Type: general
      – SubjectFull: Light scattering
        Type: general
    Titles:
      – TitleFull: Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles
        Type: main
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            NameFull: Bi, Lei
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            NameFull: Yang, Ping
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            NameFull: Kattawar, George W.
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            NameFull: Mishchenko, Michael I.
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              Text: Feb2013
              Type: published
              Y: 2013
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              Value: 116
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            – TitleFull: Journal of Quantitative Spectroscopy & Radiative Transfer
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