Physics – Optics
Scientific paper
Oct 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jqsrt..30..351k&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 30, Oct. 1983, p. 351-356.
Physics
Optics
5
Atmospheric Optics, Radiative Transfer, Spherical Harmonics, Fourier Series, Intensity, Legendre Functions, Quadratures, Series Expansion
Scientific paper
It is known that the azimuth-averaged component of the intensity computed from the spherical harmonics method for solving the equation of radiative transfer is 'exact' at the Gauss quadrature points. It is shown that a similar relation holds for higher terms in the Fourier expansion of the intensity but that the results are 'exact' at the zeros of the associated Legendre polynomials. The relationship between the discrete ordinates and spherical harmonics methods follows from this discussion. A discrete ordinates quadrature scheme, based on the zeros of the associated Legendre polynomials, is shown to maintain the correspondence of the methods for these problems, as well as providing a better set of points than other methods in use.
Karp Alan H.
Petrack S.
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