2017
DOI: 10.1016/j.jqsrt.2017.02.015
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A review of the matrix-exponential formalism in radiative transfer

Abstract: This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers approximate solution methods relying on the… Show more

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Cited by 29 publications
(20 citation statements)
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“…The solution in (10)- (11), known in Linear Algebra by the matricant [32], [39], [40], is an absolutely uniformly convergent series expansion. The series, firstly obtained by Peano, was later developed by Baker and, modernly, by Magnus, [28], [42]- [48].…”
Section: Theoretical Backgroundmentioning
confidence: 99%
“…The solution in (10)- (11), known in Linear Algebra by the matricant [32], [39], [40], is an absolutely uniformly convergent series expansion. The series, firstly obtained by Peano, was later developed by Baker and, modernly, by Magnus, [28], [42]- [48].…”
Section: Theoretical Backgroundmentioning
confidence: 99%
“…In this study, the multi-stream model is based on the discrete ordinate method with matrix exponential (DOME) [19][20][21] with 16 streams per hemisphere. Regarding the two-stream model, two comments are in order:…”
Section: Radiative Transfer Modelsmentioning
confidence: 99%
“…Equations (1) and (4a) are subject to the incoming intensity at τ =τ0 and no source incoming intensity at τ =τ1…”
Section: The Matrix Riccati Equations (Mrem) and The Interaction Prinmentioning
confidence: 99%
“…Possibilities include the multiple collision technique [7], where one partitions intensity into particle collisions whose sum is the intensity at τ and µ. This approach becomes analytically unwieldly with increasing number of collisions [1]. Another method forms integral equations for Eqs (12) and proceeds iteratively [8], which is essentially the Taylor series (TS) formulation.…”
Section: Taylor Series Representations For R and Tmentioning
confidence: 99%