Journal ArticleDOI
Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate Method
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This article is published in Journal of The Society for Industrial and Applied Mathematics.The article was published on 1960-03-01. It has received 24 citations till now. The article focuses on the topics: Ordinate & Convergence (routing).read more
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Proceedings ArticleDOI
Ray tracing volume densities
James T. Kajiya,Brian Von Herzen +1 more
TL;DR: New algorithms to trace objects represented by densities within a volume grid, e.g. clouds, fog, flames, dust, particle systems, suitable for use in computer graphics are presented.
Journal ArticleDOI
The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method
TL;DR: In this article, the authors show that whenever the discrete-ordinate method has the correct diffusion limit, both in the interior and at the boundaries, its solutions converge to the solution of the transport equation uniformly in
Journal ArticleDOI
Matrix-exponential description of radiative transfer
TL;DR: In this article, the authors apply the matrix-exponential operator technique to the radiative transfer equation in discrete form and obtain new analytical solutions for the transmission and reflection matrices in the limiting cases x ≪ 1 and x ≫ 1, where x is the optical depth of the layer.
Journal ArticleDOI
Invariant imbedding and the numerical integration of boundary-value problems for unstable linear systems of ordinary differential equations
TL;DR: An invariant imbedding technique is presented which is useful in overcoming these frequently encountered instabilities, and the results of some numerical experiments are presented.
Journal ArticleDOI
On the fundamental solution of the radiative transfer equation
TL;DR: In this paper, a general solution of the one-dimensional, azimuthally averaged radiative transfer equation in terms of a matrix exponential is presented, based on properties of matrix exponentials, including the use of the commutator and product integrals.
References
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Journal ArticleDOI
Neutron Transport Theory. By B. Davison and J. B. Sykes. 75s. 1957. (Oxford University Press)
Book
On the Inversion of Certain Matrices
TL;DR: In this article, the Lagrange interpolation formula is used for the generalized Hubert matrix for the general case of constant p. The formulas of Collar and Smith are extended here to the generalized case (1).
Journal ArticleDOI
Studies of the spherical harmonics method in neutron transport theory
TL;DR: In this article, the relation between the Gauss quadrature and the spherical harmonics method for solving the Milne problem with p-wave scattering is examined. But the relation among these two methods is not identical.