Related papers: Matrix riccati equation solution of the 1d radiati…
The development of fast numerical methods for multilevel radiative transfer (RT) applications often leads to important breakthroughs in astrophysics, because they allow the investigation of problems that could not be properly tackled using…
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
The coupled Riccati equations are cosisted of multiple Riccati-like equations with solutions coupled with each other, which can be applied to depict the properties of more complex systems such as markovian systems or multi-agent systems.…
In this paper, we proposed a new Monte Carlo radiative transport (MCRT) scheme, which is based completely on the Neumann series solution of Fredholm integral equation. This scheme indicates that the essence of MCRT is the calculation of…
Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality…
We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion…
In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a…
We show a numerical scheme to solve the moment equations of the radiative transfer, i.e., M1 model which follows the evolution of the energy density, $ E $, and the energy flux, $ \mbox{\boldmath$F$} $. In our scheme we reconstruct the…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
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…
The theory of specular X-ray reflectivity from a rough interface based upon the reflection function method (RFM) is proposed. The RFM transforms the second order differential equation for the wave amplitude into the non-linear first order…
We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…
A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the…
This paper analyzes a special instance of nonsymmetric algebraic matrix Riccati equations arising from transport theory. Traditional approaches for finding the minimal nonnegative solution of the matrix Riccati equations are based on the…
The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the…
We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative…
Light transport in graded index media follows a curved trajectory determined by the Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce…
Radial Bragg gratings are commonly used to enhance light extraction from quantum emitters, but lack a well-suited, fast simulation method for optimization beyond periodic designs. To overcome this limitation, we propose and demonstrate an…