Realistic rendering of participating media like clouds requires multiple anisotropic light scattering. This paper presents a propagation approximation for light scattered into M direction bins, which reduces the “ray effect” problem in the traditional “discrete ordinates” method. For a regular grid volume of n3 elements, it takes O(M n3 log n + M2 n3) time and O(M n3 + M2) space. This document ...

A recently developed version of the discrete-ordinates method is used along with elementary numerical linear-algebra techniques to establish an e$cient and especially accurate solution to what can be called Chandrasekhar's basic problem in radiative transfer, namely the problem of computing the radiation intensity in a "nite plane-parallel layer illuminated by an incident beam of radiation and ...

In recent years there has been increasing interest in the use of polarization for imaging objects in a cluttered environment. Examples are optical imaging through clouds, optical detection of objects in a biological medium, and microwave detection of objects in clutter. We extend previous studies of continuous-wave scattering to pulse-polarization scattering in discrete scatterers. We solve the...

A version of the discrete-ordinates method is used to solve in a unified manner some classical flow problems based on the Bhatnagar, Gross and Krook model in the theory of rarefiedgas dynamics. In particular, the thermal-creep problem and the viscous-slip (Kramers’) problem are solved for the case of a semi-infinite medium, and the Poiseuille-flow problem, the Couetteflow problem and the therma...

Abstract We present a formulation and numerical algorithm to extend the scheme for gray radiation magnetohydrodynamics (MHD) developed by Jiang include frequency dependence via multigroup approach. The entire space can be divided into an arbitrary number of groups in lab frame, we follow time-dependent evolution frequency-integrated specific intensities along discrete rays inside each group. Sp...

Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would hav...

Normalization of the scattering phase function is applied to the transient discrete ordinates method for ultrafast radiative transfer analysis in a turbid medium subject to a normal collimated incidence. Previously, the authors have developed a normalization technique which accurately conserves both scattered energy and phase function asymmetry factor after directional discretization for the He...

A new Discrete Ordinates transport solver for unstructured tetrahedral meshes is presented. The uses the Discontinuous Galërkin Finite Element Method with linear or quadratic expansion of flux within each cell. solution one-group problem obtained non-preconditioned fixed-point GMRES iterations. Precision and performances are evaluated on 3D Radiation Transport Benchmark Problems proposed by Kob...

In an earlier paper we supplied indirect proof of the existence universal possible worlds that have topological property being hypercyclic, which means they can access every world in sequences approach arbitrarily closely to world. That states there are but it does not exhibit such a explicitly. We now explicitly construct two worlds. A continuous constructs with transreal co-ordinates directly...

We present a robust and accuracy enhanced method for analyzing the propagation behavior of EM waves in z-periodic structures in (r, ö, z)-cylindrical co-ordinates. A cylindrical disk, characterized by the radius a and the periodicity length Lz, defines the fundamental cell in our problem. The permittivity of the dielectric inside this cell is characterized by an arbitrary, single-valued functio...