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Context. Three-dimensional non-local thermodynamical equilibrium (NLTE) radiative transfer calculations are a fundamental tool for a detailed spectral analysis in stellar atmospheres, but require vast amounts of computer power. This…
This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU$(2)$-nonlinear Fourier transform (NFT). The theoretical underpinnings of this generalization of the conventional…
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
We present a general formalism for computing self-consistent, numerical solutions to the time-dependent radiative transfer equation in low velocity, multi-level ions undergoing radiative interactions. Recent studies of time-dependent…
Recently, several studies proposed methods to utilize some classes of optimization problems in designing deep neural networks to encode constraints that conventional layers cannot capture. However, these methods are still in their infancy…
In the present paper we consider the full nonlocal thermodynamic equilibrium (non-LTE) radiation transfer problem. This formalism allows us to account for deviation from equilibrium distribution of both the radiation field and the massive…
Context - Exoplanetary upper atmospheres are low density environments where radiative processes can compete with collisional ones and introduce non-local thermodynamic equilibrium (NLTE) effects into transmission spectra. Aims - We develop…
Thermal radiative transfer (TRT) is an essential piece of physics in inertial confinement fusion, high-energy density physics, astrophysics etc. The physical models of this type of problem are defined by strongly coupled differential…
The improvement in observational facilities requires refining the modelling of the geometrical structures of astrophysical objects. Nevertheless, for complex problems such as line overlap in molecules showing hyperfine structure, a detailed…
We have developed an algorithm for transferring radiation in three-dimensional space. The algorithm computes radiation source and sink terms using the Fast Fourier Transform (FFT) method, based on a formulation in which the integral of any…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
The sequential fully implicit (SFI) method was introduced along with the development of the multiscale finite volume (MSFV) framework, and has received considerable attention in recent years. Each time step for SFI consists of an outer loop…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
Photoacoustic tomography (PAT) is a promising imaging technique that can visualize the distribution of chromophores within biological tissue. However, the accuracy of PAT imaging is compromised by light fluence (LF), which hinders the…
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary problems. Their solution via differential equations implies to make hypotheses on the solution itself, namely…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
Modeling the variability of the solar spectral irradiance is a key factor for understanding the solar influence on the climate of the Earth. As a first step to calculating the solar spectral irradiance variations we reproduce the solar…
This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…