Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport
Abstract
The discrete ordinates discontinuous Galerkin (SN-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind SN-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original SN-DG method, the low-memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in the scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. Finally, for both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.
- Authors:
-
[1];
[2]
- The Ohio State Univ., Columbus, OH (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- OSTI Identifier:
- 1902799
- Grant/Contract Number:
- AC05-00OR22725; SC0014664
- Resource Type:
- Accepted Manuscript
- Journal Name:
- SIAM Journal on Scientific Computing
- Additional Journal Information:
- Journal Volume: 42; Journal Issue: 4; Journal ID: ISSN 1064-8275
- Publisher:
- Society for Industrial and Applied Mathematics (SIAM)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; radiative transport; discrete ordinates; discontinuous Galerkin; diffusion limit
Citation Formats
Sun, Zheng, and Hauck, Cory D. Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport. United States: N. p., 2020.
Web. doi:10.1137/19m1271956.
Sun, Zheng, & Hauck, Cory D. Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport. United States. https://doi.org/10.1137/19m1271956
Sun, Zheng, and Hauck, Cory D. Thu .
"Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport". United States. https://doi.org/10.1137/19m1271956. https://www.osti.gov/servlets/purl/1902799.
@article{osti_1902799,
title = {Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport},
author = {Sun, Zheng and Hauck, Cory D.},
abstractNote = {The discrete ordinates discontinuous Galerkin (SN-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind SN-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original SN-DG method, the low-memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in the scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. Finally, for both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.},
doi = {10.1137/19m1271956},
journal = {SIAM Journal on Scientific Computing},
number = 4,
volume = 42,
place = {United States},
year = {Thu Jul 02 00:00:00 EDT 2020},
month = {Thu Jul 02 00:00:00 EDT 2020}
}
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