On multi-region problems in radiative transfer

Devaux, C.; Grandjean, P.; Ishiguro, Yukio; Siewert, C. E.

doi:10.1007/bf00643916

Cited by 37 publications

(2 citation statements)

References 6 publications

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“…There are about "nineteen dubious ways" [13] to evaluate a matrix exponential. One popular representation is through matrix diagonalization, which corresponds to the ADO and response matrix-like methods [15][16][17] that require eigenvalues and eigenvectors of A. If one desires precision through simplicity, it is best to use a numerical scheme free of eigenvalues and eigenvectors.…”

Section: A Evaluation Of the Matrix Exponentialmentioning

confidence: 99%

A 1D radiative transfer benchmark with polarization via doubling and adding

Ganapol

2017

Journal of Quantitative Spectroscopy and Radiative Transfer

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Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to 7 places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

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Section: A Evaluation Of the Matrix Exponentialmentioning

confidence: 99%

A 1D radiative transfer benchmark with polarization via doubling and adding

Ganapol

2017

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…A first verification considers a Mie scattering benchmark for the (L = 8) with the phase function given by the following scattering coefficients [6]:  varying over 0.9, 0.99 and 0.999. The results are in complete agreement with those of the benchmark [6]. To provide a more complete benchmark, we extend the results by two digits and include the total R f +T n for later use.…”

Section:  mentioning

confidence: 99%

The response matrix discrete ordinates solution to the 1D radiative transfer equation

Ganapol

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme accuracy as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey-Greenstein scattering as an example.

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The Art of Analytical Benchmarking

Ganapol

Furfaro

2008

Lecture Notes in Computational Science and Engineering

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On multi-region problems in radiative transfer

Cited by 37 publications

References 6 publications

A 1D radiative transfer benchmark with polarization via doubling and adding

A 1D radiative transfer benchmark with polarization via doubling and adding

The response matrix discrete ordinates solution to the 1D radiative transfer equation

The Art of Analytical Benchmarking

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