相关论文: Formal solutions for polarized radiative transfer.…
The standard formula, due to Spiegel, for the smoothing of temperature fluctuations by radiative transfer is unstable in relativity. This is due to the fact that Spiegel neglected the transit time of light, thereby allowing the transport…
Radiative transfer simulations are now at the forefront of numerical astrophysics. They are becoming crucial for an increasing number of astrophysical and cosmological problems; at the same time their computational cost has come to the…
Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate…
Evolving the size distribution of solid aggregates challenges simulations of young stellar objects. Among other difficulties, generic formulae for stability conditions of explicit solvers provide severe constrains when integrating the…
Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially…
We study the quantitative transfer of uniqueness from the classical to the fractional Calder\'on problem with exterior data. This allows us to deduce the first stability estimates for the principal part of the isotropic fractional…
In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system coupled with Poisson or Amp\`ere equation. Splitting methods…
The radiative instability of a beam moving in a photonic crystal of finite dimensions is studied. The dispersion equation is obtained. The law $\Gamma\sim \rho ^{1/\left( {s + 3} \right)}$ is shown to be valid and caused by the mixing of…
Accurate accounting of particle number and 4-momentum in radiative transfer may be facilitated by the use of transport equations that allow transparent conversion between volume and surface integrals in both spacetime and momentum space.…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
We analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of…
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…
Many time-dependent differential equations are equipped with invariants. Preserving such invariants under discretization can be important, e.g., to improve the qualitative and quantitative properties of numerical solutions. Recently,…
This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the…
We revisit the instability properties of the recovery of the absorption coefficient for the radiative transfer equation in the diffusive regime. To this end, we develop a rather robust framework building on [Koch-R\"uland-Salo, 2021] which…
Linearized numerical stability bounds for solving the nonlinear time-dependent Schr\"odinger equation (NLSE) using explicit finite-differencing are shown. The bounds are computed for the fourth-order Runge-Kutta scheme in time and both…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…
A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, the solution of…
In this paper we consider the stabilization of non-fundamental unstable stationary solutions of the cubic nonlinear Schrodinger equation. Specifically we study the stabilization of radially symmetric solutions with nodes and asymmetric…