相关论文: Numerical analysis of a hybrid method for radiatio…
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this…
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…
We present a new algorithm to solve the equations of radiation hydrodynamics (RHD) in a frequency-integrated, two-moment formulation. Novel features of the algorithm include i) the adoption of a non-local Variable Eddington Tensor (VET)…
Context: Dynamical studies of irradiated circumstellar disks require an accurate treatment of radiation transport to, for example, properly determine cooling and fragmentation properties. The radiation transport algorithm should be as fast…
Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…
Thermal radiative transfer (TRT) presents significant computational challenges due to the stiff, nonlinear coupling between radiation and material energy, particularly in multigroup, high-fidelity transport models. In this work, we develop…
The electron and photon transport processes in spectroscopy techniques described by the invariant embedding theory is here revisited. We report a convergence method to obtain closed analytical solutions to the 3D integro-differential…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
In this work we develop an approach for a molecular hydrogen ion (H2+) in the Born-Oppenheimer approximation while exposed to intense short-pulse radiation. Our starting point is the R-Matrix incorporating Time (RMT) formulation for atomic…
We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…
Resonance spectral lines such as H I Ly {\alpha}, Mg II h&k, and Ca II H&K that form in the solar chromosphere are influenced by the effects of 3D radiative transfer as well as partial redistribution (PRD). So far no one has modeled these…
We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based…
We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path-length $s$), and models particle transport…
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…
Radiation is crucial not only for observing astrophysical objects, but also for transporting energy and momentum. However, accurate on-the-fly radiation transport in astrophysical simulations is challenging and computationally expensive.…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi-dimensional RTE with rotated reference frames.