Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering
Abstract
Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.
- Authors:
-
- California State University, Bakersfield, CA (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- OSTI Identifier:
- 1838952
- Grant/Contract Number:
- AC05-00OR22725; 1217170
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Mathematics of Computation
- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 332; Journal ID: ISSN 0025-5718
- Publisher:
- American Mathematical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Sheng, Qiwei, and Hauck, Cory D. Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering. United States: N. p., 2021.
Web. doi:10.1090/mcom/3670.
Sheng, Qiwei, & Hauck, Cory D. Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering. United States. https://doi.org/10.1090/mcom/3670
Sheng, Qiwei, and Hauck, Cory D. Mon .
"Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering". United States. https://doi.org/10.1090/mcom/3670. https://www.osti.gov/servlets/purl/1838952.
@article{osti_1838952,
title = {Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering},
author = {Sheng, Qiwei and Hauck, Cory D.},
abstractNote = {Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.},
doi = {10.1090/mcom/3670},
journal = {Mathematics of Computation},
number = 332,
volume = 90,
place = {United States},
year = {Mon Jul 19 00:00:00 EDT 2021},
month = {Mon Jul 19 00:00:00 EDT 2021}
}
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