Related papers: Exact solutions for radiative transfer with partia…
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical…
A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to…
In the central part of this paper, we revisit the classical study of the H-function defined as the unique solution, regular in the right complex half-plane, of a Cauchy integral equation. We take advantage of our work on the N-function…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the…
Two-frequency radiative transfer (2f-RT) theory is developed for classical waves in random media. Depending on the ratio of the wavelength to the scale of medium fluctuation 2f-RT equation is either a Boltzmann-like integral equation with a…
We present two new accurate and efficient method to compute the formal solution of the polarized radiative transfer equation. In this work, the source function and the absorption matrix are approximated using quadratic and cubic Bezier…
We present the first extension of the special-relativistic Lattice-Boltzmann Method for radiative transport developed by Weih et al. (2020), to solve the radiative-transfer equation in curved spacetimes. The novel approach is based on the…
A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
In the present article, we discuss a numerical method of solution for the so-called "full non-LTE" radiation transfer problem, basic formalism of which was revisited by Paletou & Peymirat (2021; see also Oxenius 1986). More specifically,…
We introduce a layer potential representation for the solution of the transmission problem defined by two dielectric channels, or open wave-guides, meeting along the straight-line interface, $\{x_1=0\}.$ The main observation is that the…
In this paper we present a characteristic method for solving the transfer equation in differentially moving media in a curved spacetime. The method is completely general, but its capabilities are exploited at best in presence of symmetries,…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
In this work we study the radiative transfer equation in the forward-peaked regime in free space. Specifically, it is shown that the equation is well-posed by proving instantaneous regularization of weak solutions for arbitrary initial…
We study the standard spectral line radiative transfer equation for media consisting of resonant atoms and non-resonant components (the dust grains and the atoms without considered spectral transition). Our goal is to study the intensity…