相关论文: Accuracy Controlled Schemes for the Eigenvalue Pro…

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the…

We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the integral operator in this formulation…

The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…

Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order…

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…

We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…

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…

This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…

We propose a new approach to the numerical solution of radiative transfer equations with certified a posteriori error bounds. A key role is played by stable Petrov--Galerkin type variational formulations of parametric transport equations…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

Radiative corrections to reactions involving atoms or nuclei can become sensitive to the structure of the bound state. Generically, one encounters correlation functions of multiple currents which must satisfy Ward identities. At…

Achieving efficient and accurate simulation of the radiative transfer has long been a research challenge. Here we introduce the general synthetic iterative scheme as an easy-to-implement approach to address this issue. First, a macroscopic…

Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they are yet to be implemented and applied in…

Many types of neutron spectrometer use a conventional primary spectrometer consisting of some collimator, a crystal monochromator and a second collimator. Conventional resolution descriptions use instrument parameter values to deduce the…

We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino…

The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or…

The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…

The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear…