Related papers: Numerical Solution of the Expanding Stellar Atmosp…
The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
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…
We derive a (1+1)-dimensional nonlinear evolution equation (NLE) which may model the propagation of high-frequency perturbations in a relaxing medium. As a result, this equation may possess three typical solutions depending on a dissipative…
We consider a PDE approach to numerically solving the reflector antenna problem by solving an Optimal Transport problem on the unit sphere with cost function $c(x,y) = -2\log \left\Vert x - y \right\Vert$. At each point on the sphere, we…
(Abridged) In this paper we present a compilation of results from our most advanced neutron star merger simulations, including a description of the employed numerical procedures and a more complete overview over a large number of computed…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
We consider the iterative solution of anisotropic radiative transfer problems using residual minimization over suitable subspaces. We show convergence of the resulting iteration using Hilbert space norms, which allows us to obtain…
Large-scale stellar surveys, such as SDSS-V, 4MOST, WEAVE, and PLATO, require accurate atmospheric models and synthetic spectra of stars for accurate analyses of fundamental stellar parameters and chemical abundances. The primary goal of…
Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an $N$-level model atom, the technique avoids the $N^{3}$ scaling in…
In this paper, we describe a multiscale model based on magneto-static traps of neutral atoms or ion traps. The idea is to levitate a magnetic spinning top in the air repelled by a base magnet. For such a problem, we have to deal with…
Context. B-type supergiants are versatile tools to address various astrophysical topics, ranging from stellar atmospheres over stellar and galactic evolution to the cosmic distance scale. Aims. A hybrid non-LTE approach - line-blanketed…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
The status of numerical hydrodynamical models for Planetary Nebulae is reviewed. Since all of the numerical work is based on the interacting winds model, we start with a description of this model and give an overview of the early analytical…
A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
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: State of the art quantitative spectroscopy of OB-stars compares synthetic spectra (calculated by means of 1D, spherically symmetric computer codes) with observations. Certain stellar atmospheres, however, show strong deviations…
We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers…