Convergence of filtered spherical harmonic equations for radiation transport
Abstract
In this work, we analyze the global convergence properties of the filtered spherical harmonic (FPN) equations for radiation transport. The well-known spherical harmonic (PN) equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the global $L^2$ convergence rate (in space and angle) of the spectral method to the solution of the transport equation depends on the smoothness of the solution (in angle only) and on the order of the filter. The results are confirmed by numerical experiments. Numerical tests have been implemented in MATLAB and are available online.
- Authors:
-
[2];
- RWTH Aachen Univ. (Germany)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)
- OSTI Identifier:
- 1845815
- Grant/Contract Number:
- AC05-00OR22725; 1217170; 11-07291
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Communications in Mathematical Sciences
- Additional Journal Information:
- Journal Volume: 14; Journal Issue: 5; Journal ID: ISSN 1539-6746
- Publisher:
- International Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; spectral filtering; spherical harmonics; radiation transport
Citation Formats
Frank, Martin, Hauck, Cory, and Küpper, Kerstin. Convergence of filtered spherical harmonic equations for radiation transport. United States: N. p., 2016.
Web. doi:10.4310/cms.2016.v14.n5.a10.
Frank, Martin, Hauck, Cory, & Küpper, Kerstin. Convergence of filtered spherical harmonic equations for radiation transport. United States. https://doi.org/10.4310/cms.2016.v14.n5.a10
Frank, Martin, Hauck, Cory, and Küpper, Kerstin. Wed .
"Convergence of filtered spherical harmonic equations for radiation transport". United States. https://doi.org/10.4310/cms.2016.v14.n5.a10. https://www.osti.gov/servlets/purl/1845815.
@article{osti_1845815,
title = {Convergence of filtered spherical harmonic equations for radiation transport},
author = {Frank, Martin and Hauck, Cory and Küpper, Kerstin},
abstractNote = {In this work, we analyze the global convergence properties of the filtered spherical harmonic (FPN) equations for radiation transport. The well-known spherical harmonic (PN) equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the global $L^2$ convergence rate (in space and angle) of the spectral method to the solution of the transport equation depends on the smoothness of the solution (in angle only) and on the order of the filter. The results are confirmed by numerical experiments. Numerical tests have been implemented in MATLAB and are available online.},
doi = {10.4310/cms.2016.v14.n5.a10},
journal = {Communications in Mathematical Sciences},
number = 5,
volume = 14,
place = {United States},
year = {Wed May 18 00:00:00 EDT 2016},
month = {Wed May 18 00:00:00 EDT 2016}
}
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Filtered Discrete Ordinates Equations for Radiative Transport
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- Laiu, M. Paul; Hauck, Cory D.
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