Related papers: A pseudospectral method for solution of the radiat…
Radiative transfer is a fundamental process in astrophysics, essential for both interpreting observations and modeling thermal and dynamical feedback in simulations via ionizing radiation and photon pressure. However, numerically solving…
We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean free path is of order of the system size. Within the accuracy of the single-scattering approximation to the radiative transport equation,…
Path-Guiding algorithms for sampling scattering directions can drastically decrease the variance of Monte Carlo estimators of Light Transport Equation, but their usage was limited to offline rendering because of memory and computational…
We present a novel extension of the path tracing algorithm that is capable of treating highly scattering participating media in the presence of fluorescent structures. The extension is based on the formulation of the full radiative transfer…
An improvement modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The main focus of the modified SA lies on a slight modification of the…
Biological tissues are complex structures composed of many elements which make light-based tissue diagnostics challenging. Over the past decades, Monte Carlo technique has been used as a fundamental and versatile approach toward modeling…
The high computational expense of simulating light through ray-tracing in large, sparsely instrumented particle detectors such as IceCube and Antares is a critical outstanding problem in particle physics. When the detector is sparsely…
A new Monte-Carlo algorithm for calculating time-dependent radiative-transfer under the assumption of LTE is presented. Unlike flux-limited diffusion the method is polychromatic, includes scattering, and is able to treat the optically thick…
We present the Eulerian Gaussian beam method in anisotropic media. We derive kinematic and dynamic ray tracing equations based on the level set theory and Eulerian theory using the anisotropic eikonal equation. Compared with the traditional…
Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative…
An asymptotic analysis is used to derive a set of diffusion approximations to the nonclassical transport equation with isotropic scattering. These approximations are shown to reduce to the simplified P$_N$ equations under the assumption of…
Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific…
The steady-state simplified $P_N$ approximation to the radiative transport equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified $P_N$ equations have been derived by an asymptotic…
A novel method for monochromatic scalar 3D radiative transfer, designed primarily for modeling remote sensing imaging, is presented. For simulating an observation of an imaging satellite instrument, the method uses a heuristic scattering…
Networks of interconnected resistors, springs and beams, or pores are standard models of studying scalar and vector transport processes in heterogeneous materials and media, such as fluid flow in porous media, and conduction, deformations,…
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 study evolution equations with non-self-adjoint generators, for example the convection-diffusion equation. Spectral expansions are not a reliable method of solving such equations, because they are so ill-conditioned. We introduce a new…
In this paper, we propose a space-time GMsFEM for transport equations. Multiscale transport equations occur in many geoscientific applications, which include subsurface transport, atmospheric pollution transport, and so on. Most of existing…
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…
We have investigated the transport of light through slabs that both scatter and strongly absorb, a situation that occurs in diverse application fields ranging from biomedical optics, powder technology, to solid-state lighting. In…