Matrix exponential in C/C++ version of vector radiative transfer code IPOL

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https://www.sciencedirect.com/science/article/pii/S0022407319300123

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https://doi.org/10.1016/j.jqsrt.2019.02.009
 http://hdl.handle.net/11603/28818

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Author/Creator ORCID

https://orcid.org/0000-0003-4690-3232

Date

2019-02-13

Type of Work

journal articles
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Citation of Original Publication

Korkin, Sergey and Alexei Lyapustin. "Matrix exponential in C/C++ version of vector radiative transfer code IPOL." Journal of Quantitative Spectroscopy and Radiative Transfer 227 (April, 2019): 106-110. https://doi.org/10.1016/j.jqsrt.2019.02.009.

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This work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
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Abstract

We use only left eigenvectors to evaluate the matrix exponential in the method of discrete ordinates for the vector radiative transfer equation, which neglects circular polarization, in a plane-parallel atmosphere. This is contrary to a common practice of using the right eigenvectors to evaluate the matrix exponential combined with the left eigenvectors to avoid the inversion of the matrix of the right ones. Two numerical tests for Rayleigh and Aerosol scattering confirm our idea. For better explanation of our approach and for independent crosscheck of our results, we distribute an example in C/C++.