Related papers: On Broyden's method for the solution of the multil…
In this paper we present a multilevel projection-based iterative scheme for solving thermal radiative transfer problems that performs iteration cycles on the high-order Boltzmann transport equation (BTE) and low-order moment equations.…
A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer.…
We describe a highly flexible framework to solve 3D radiation transfer problems in scattering dominated environments based on a long characteristics piece-wise parabolic formal solution and an operator splitting method. We find that the…
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 paper, we propose the greedy and random Broyden's method for solving nonlinear equations. Specifically, the greedy method greedily selects the direction to maximize a certain measure of progress for approximating the current…
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…
Non-LTE radiative transfer is a key tool for modern astrophysics: it is the means by which many key synthetic observables are produced, thus connecting simulations and observations. Radiative transfer models also inform our understanding of…
The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest…
Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the…
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…
Since the mass of the electron is very small relative to atomic masses, Thomson scattering of low-energy photons ($h\nu \ll m_ec^2$) produces thermal Doppler frequency shifts that are much larger than atomic Doppler widths. A method is…
We test the accuracy of the ALI method, widely used in stellar atmosphere modelling, by solving exactly a standard radiative transfer problem in plane-parallel geometry. Some recommendations are given for a practical use of this method.
The so-called full non-local thermodynamic equilibrium (FNLTE) radiative transfer problem allows us to take into account not only deviations of the radiation field from the Planckian but also deviations of the densities and velocity…
Context. Computing spectra from 3D simulations of stellar atmospheres when allowing for departures from local thermodynamic equilibrium (non-LTE) is computationally very intensive. Aims. We develop a machine learning based method to speed…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…
We consider the problem of solving linear systems of equations arising with limited-memory members of the restricted Broyden class of updates and the symmetric rank-one (SR1) update. In this paper, we propose a new approach based on a…
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…
In this paper, we study the explicit superlinear convergence rates of quasi-Newton methods. We particularly focus on the classical Broyden's method for solving nonlinear equations. We establish its explicit (local) superlinear convergence…
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,…