Related papers: Solution of NLTE Radiative Transfer Problems Using…
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…
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,…
This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently…
This review presents basic equations for the solution of the NLTE radiative transfer problem for trace elements and methods for its solution are summarized. The importance of frequency coupling in radiative transfer in stellar atmospheres…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
In this paper, we reveal the intrinsic Toeplitz structure in the unique stabilizing solution for nonsymmetric algebraic Riccati equations by employing a shift-involved fixed-point iteration, and propose an RADI-type method for computing…
This paper considers blind inverse image restoration, the task of predicting a target image from a degraded source when the degradation (i.e. the forward operator) is unknown. Existing solutions typically rely on restrictive assumptions…
We describe a new algorithm to solve the time dependent, frequency integrated radiation transport (RT) equation implicitly, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using {\sf Athena++}. The…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
The efficient numerical solution of Non-LTE multilevel transfer problems requires the combination of highly convergent iterative schemes with fast and accurate formal solution methods of the radiative transfer (RT) equation. This…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a subsequence of the sequence of iterates generated converges…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches…
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…
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature,…
We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize…
In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is particularly efficient when coupled with a recently-introduced…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann…