Fast iterative methods for discrete-ordinates particle transport calculations

Adams, Marvin L.; Larsen, Edward W.

doi:10.1016/s0149-1970(01)00023-3

Cited by 442 publications

(292 citation statements)

References 115 publications

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“…For the regular part we use quasi two-stream approximation. This method is a special case of the synthetic iterations method proposed in nuclear physics (Adams and Larsen, 2002). Now we apply it in radiative transfer theory.…”

Section: Proposed Solutionmentioning

confidence: 99%

The Mathematical Model of Optical Remote Sensing System Signal Considering Broken Cloudiness Effects

Budak

Shagalov

2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:With increasing of the accuracy of measuring equipment for the optical remote sensing in recent years the requirements for speed and accuracy of the algorithms for satellite data processing has greatly increased. It became necessary accurately to account all of the known factors, which affect the signal significantly. At each time, more than half of the planet is covered with clouds, so it is almost always necessary to take measurements into breaks in clouds. Cloudiness is among those factors which affect significantly the signal and its neglect in extreme cases can lead to an error of 140%. Here we propose a new solution of the radiative transfer equation (RTE) for a slab of a turbid medium with consideration of broken clouds. We use the classical approach to solving RTE: complete solution is represented as the sum of the anisotropic and regular parts. We express anisotropic part using small-angle modification of the spherical harmonics method. For the regular part we propose to use quasi two-stream approximation. This method is a special case of the synthetic iterations method. The method is based on splitting the ordinary iteration into two stages. At the first step one of approximate methods is used, and on the second step one ordinary iteration is used. We use two-stream approximation as an approximate method. In this paper we proposed a solution for the simplest case of broken clouds -cylindrical hole in the slab. Comparison of the algorithm was performed with established program MDOM, and showed good agreement.

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Section: Proposed Solutionmentioning

confidence: 99%

The Mathematical Model of Optical Remote Sensing System Signal Considering Broken Cloudiness Effects

Budak

Shagalov

2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…In nuclear physics [4] a method of synthetic iterations (SI) is suggested. Using the SI ideas it is possible to increase significantly the accuracy of calculations for smaller N. By SI each step of iterations is divided into two steps [4]: at the first step the approximate angular distribution of the RTE solution is sought, and at the second step it is specified by the algorithm of standard iteration.…”

Section: Synthetic Iterationsmentioning

confidence: 99%

“…Using the SI ideas it is possible to increase significantly the accuracy of calculations for smaller N. By SI each step of iterations is divided into two steps [4]: at the first step the approximate angular distribution of the RTE solution is sought, and at the second step it is specified by the algorithm of standard iteration. Since MDOM provides fast convergence in means by power, we can expect a substantial acceleration of the calculation of RAD when using synthetic iterations.…”

Section: Synthetic Iterationsmentioning

confidence: 99%

Solution of the radiative transfer equation by eliminating the anisotropic part within the method of synthetic iteration

Budak

Shagalov

2013

AIP Conference Proceedings

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“…To understand this phenomenon and theoretically predict the convergence properties of linear transport iteration methods, problems with spatially periodic heterogeneous media have been studied by means of a Fourier analysis [1,5,2]. There exists a group of nonlinear methods for solving transport problems [4,5].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Anistratov¹,

Constantinescu²,

Roberts³

et al. 2007

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Fast iterative methods for discrete-ordinates particle transport calculations

Cited by 442 publications

References 115 publications

The Mathematical Model of Optical Remote Sensing System Signal Considering Broken Cloudiness Effects

The Mathematical Model of Optical Remote Sensing System Signal Considering Broken Cloudiness Effects

Solution of the radiative transfer equation by eliminating the anisotropic part within the method of synthetic iteration

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

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