Related papers: A fast algorithm for radiative transport in isotro…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
We study the approximation of the radiative transfer equation with a relatively few moments in the spherically symmetric case. We propose a three-moment model based on choosing the beta distribution as the ansatz for the specific intensity.…
We propose a new fast algorithm optimized for full-wave electromagnetic (EM) scattering analysis of a large-scale cloud of chaffs with arbitrary orientation, spatial distribution, and length. By leveraging the unique EM scattering…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…
Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an accelerated Schwarz method for radiative transfer equations…
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the…
We describe a highly flexible framework to solve 3D radiation transfer problems in scattering dominated environments based on a long characteristics piece-wise parabolic formal solution and an operator splitting method. We find that the…
We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code {\small GADGET}. It is based on a fast, robust and photon-conserving integration scheme where the…
Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the…
This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological…
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.
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
We simulate convection near the solar surface, where the continuum optical depth is of order unity. Hence, to determine the radiative heating and cooling in the energy conservation equation, we must solve the radiative transfer equation…
The basic idea of an extremely fast convergent iterative method, the Forth-and-Back Implicit Lambda Iteration (FBILI), is briefly described and the applications of the method to various RT problems are listed and discussed.
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…
In this paper we discuss numerical methods and algorithms for the solution of NLTE stellar atmosphere problems involving expanding atmospheres, e.g., found in novae, supernovae and stellar winds. We show how a scheme of nested iterations…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…