Related papers: A fast algorithm for radiative transport in isotro…
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…
The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently…
We have developed an algorithm for transferring radiation in three-dimensional space. The algorithm computes radiation source and sink terms using the Fast Fourier Transform (FFT) method, based on a formulation in which the integral of any…
This paper presents nonlinear iterative methods for the fundamental thermal radiative transfer (TRT) model defined by the time-dependent multifrequency radiative transfer (RT) equation and the material energy balance (MEB) equation. The…
We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…
Fast, high-order accurate algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied…
We present a numerical method for solving the time-independent thermal radiative transfer (TRT) equation or the neutron transport (NT) equation when the opacity or cross-section varies rapidly in energy (frequency). The approach is based on…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
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…
A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
Radiative transfer calculations are essential for modeling planetary atmospheres. However, standard methods are computationally demanding and impose accuracy-speed trade-offs. High computational costs force numerical simplifications in…
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…
Accurate photometric and kinematic modelling of disc galaxies requires the inclusion of radiative transfer models. Due to the complexity of the radiative transfer equation (RTE), sophisticated techniques are required. Various techniques…
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 letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are…
A nonsingular analytical solution for the transfer equation in a pure absorber is obtained in central symmetry and in a monochromatic radiation field. The native regular singularity of the equation is removed by applying a linear…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…