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This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting semi-...

This paper proposes a unified gas-kinetic particle (UGKP) method for the frequency-dependent photon transport process. The photon transport is a typical multiscale process governed by the nonlinear radiative transfer equations (RTE). The flow ...

The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radiation diffusion and frequency-dependent diffusion ...

• The frequency discretization can be consistent with the required multi-group diffusion model.

We propose two spatial second-order schemes for linear radiative transfer equations by using the idea of the unified gas kinetic scheme (UGKS) to construct the numerical boundary fluxes, and show that the proposed schemes are both positive and ...

The generalized polynomial chaos (gPC) method is one of the most popular method for uncertainty quantification. Being essentially a spectral approach, the gPC method exhibits the spectral convergence rate which heavily depends on the regularity of ...

This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation. In our previous work (Huang et al. in J Comput Phys 453:110941, 2022), we proposed an approach to learn the ...${}_{}$

We present an asymptotic preserving method for the radiative transfer equations in the framework of $P_N$ method. An implicit and explicit numerical scheme is proposed to solve the $P_N$ system based on the order analysis of the expansion coefficients ...${}_{}$

In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for the radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly ...

• We apply machine learning to the moment closure for the radiative transfer equation.

In this paper, we propose and analyze a spherical harmonic discontinuous Galerkin (SH-DG) method for solving the radiative transfer equations with vacuum boundary conditions. To incorporate vacuum boundary conditions in spherical harmonic ...

We consider a stationary boundary value problem describing a radiative–conductive heat transfer in a semitransparent body with absolutely black inclusions. To describe the radiative transfer, the integro-differential radiative transfer equation is ...

A novel multiple-relaxation-time (MRT) lattice Boltzmann model is proposed for the radiative transfer equation (RTE). In this paper, the discussion and implementation are restricted to the grey (frequency-independent) radiative ...

This paper is concerned with the approximation of the radiative transfer equation for a grey medium in the slab geometry by the moment method. We develop a novel moment model inspired by the classical P N model and M N model. The new ...

• Propose a novel nonlinear moment model for RTE in slab geometry.
• Investigate ...

Two Krylov subspace methods, the GMRES and the BiCGSTAB, are analyzed for solving the linear systems arising from the mixed finite element discretization of the discrete ordinates radiative transfer equation. To increase their ...

This paper considers an accurate and efficient numerical scheme for solving the radiative transfer equation (RTE) based on the discrete ordinates method (DOM) in highly forward-peaked scattering media. The DOM approximates the ...

• We renormalize the highly forward-peaked phase function at the first order.
• We ...

We further investigate the high order positivity-preserving discontinuous Galerkin (DG) methods for linear hyperbolic and radiative transfer equations developed in Yuan et al. (SIAM J Sci Comput 38:A2987---A3019, 2016). The DG methods in Yuan et al. (...

In this paper we study the stationary radiative transfer equation with random coefficients. Galerkin methods are applied, which use orthogonal polynomials associated with the probability distribution of the random variables as basis functions in the ...

The radiative transfer equation (RTE) arises in a wide variety of applications. In certain situations, the energy dependence is not negligible. In a series of two papers, we study the energy dependent RTE. In this first paper of the series, we focus on ...

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature ...

This paper presents a fast and optimal multigrid solver for the radiative transfer equation. A discrete-ordinate discontinuous-streamline diffusion method is employed to discretize the radiative transfer equation. Instead of utilizing conventional ...

We study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel ...