The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the estimation of the remainder. The Hilbert expansion has to be done up to order 3 to overcome some difficulties caused by the random noise.

In this work we consider the numerical solution of a radiative transfer equation for modeling the emission of photons in stellar atmospheres. Mathematically, the problem is formulated in terms of a weakly singular Fredholm integral equation defined on a Banach space. Computational approaches to solve the problem are discussed, using direct and iterative strategies that are implemented in open s...

We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures which include dense regions of high optical depth like in dense molecular clouds, circumstellar disks, envelopes of evolved stars, and dust tori around active galactic nuclei. The corresponding continuum radiative transfer problem is described and the numerical requirements for invers...

We describe a novel adaptive ray tracing scheme to solve the equation of radiative transfer around point sources in hydrodynamical simulations. The angular resolution adapts to the local hydrodynamical resolution and hence is of use for adaptive meshes as well as adaptive smooth particle hydrodynamical simulations. Recursive creation of rays ensures ease of implementation. The multiple radial i...

The Modular Inversion Program (MIP) is a processing and development tool designed for retrieval and mapping of hydro-biological parameters obtained from multiand hyperspectral remote sensing measurements. The architecture of the program binds a set of general and transferable computational schemes in a chain, connecting bio-physical parameters with the measured reflected radiance. The radiative...

This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Ga...

In this study transient radiative heat transfer is investigated in scattering, absorbing, and emitting media. The radiation element method is formulated for the first time to solve the transient radiative transfer equation in 3-D geometries. The sensitivity and accuracy of the method are examined. A good agreement of temporal transmittance predicted by the present method and Monte Carlo method ...

Relativistic radiative transfer problems require the calculation of photon trajectories in curved spacetime. We present a novel technique for rapid and accurate calculation of null geodesics in the Kerr metric. The equations of motion from the Hamilton-Jacobi equation are reduced directly to Carlson’s elliptic integrals, simplifying algebraic manipulations and allowing all coordinates to be com...

Recent advances in biomedicine involving the use of ultrashort pulsed laser technology, including such applications as optical tomography and plasma-mediated ablation, have mandated the necessity of accurately modeling ultrafast propagation of radiant energy through solution of the timedependent equation of radiative transfer. Numerical modeling can be implemented as a realistic alternative for...

Optimal control problems for radiative transfer and for approximate models are considered. Following the approach first discretize, then optimize, the discrete SPN approximations are for the first time derived exactly, which can be used to study optimal control on reduced order models. Combining asymptotic analysis and the adjoint calculus yields diffusive-type approximations for the adjoint ra...