Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

Sun, Zheng; Hauck, Cory D.

doi:10.1137/19m1271956

Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

Journal Article · Thu Jul 02 00:00:00 EDT 2020 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/19m1271956· OSTI ID:1902799

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The Ohio State Univ., Columbus, OH (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: AC05-00OR22725; SC0014664

OSTI ID:: 1902799

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 4 Vol. 42; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

References (19)

Diffusion approximation and computation of the critical size Bardos, C.; Santos, R.; Sentis, R. Transactions of the American Mathematical Society, Vol. 284, Issue 2 https://doi.org/10.1090/s0002-9947-1984-0743736-0	journal	February 1984
On Locking and Robustness in the Finite Element Method Babuška, Ivo; Suri, Manil SIAM Journal on Numerical Analysis, Vol. 29, Issue 5 https://doi.org/10.1137/0729075	journal	October 1992
A Mixed Variational Framework for the Radiative Transfer Equation Egger, Herbert; Schlottbom, Matthias Mathematical Models and Methods in Applied Sciences, Vol. 22, Issue 03 https://doi.org/10.1142/s021820251150014x	journal	March 2012
Boundary layers and homogenization of transport processes Bensoussan, Alain; Lions, Jacques-L.; Papanicolaou, George C. Publications of the Research Institute for Mathematical Sciences, Vol. 15, Issue 1 https://doi.org/10.2977/prims/1195188427	journal	January 1979
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms Jin, Shi; Levermore, C. David Journal of Computational Physics, Vol. 126, Issue 2 https://doi.org/10.1006/jcph.1996.0149	journal	July 1996
Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation Wu, Lei; Guo, Yan Communications in Mathematical Physics, Vol. 336, Issue 3 https://doi.org/10.1007/s00220-015-2315-y	journal	February 2015
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes Larsen, Edward W.; Morel, J. E.; Miller, Warren F. Journal of Computational Physics, Vol. 69, Issue 2 https://doi.org/10.1016/0021-9991(87)90170-7	journal	April 1987
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II larsen, Edward W.; Morel, J. E. Journal of Computational Physics, Vol. 83, Issue 1 https://doi.org/10.1016/0021-9991(89)90229-5	journal	July 1989
A robust S-DG-approximation for radiation transport in optically thick and diffusive regimes Ragusa, J. C.; Guermond, J. -L.; Kanschat, G. Journal of Computational Physics, Vol. 231, Issue 4 https://doi.org/10.1016/j.jcp.2011.11.017	journal	February 2012
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems Cockburn, Bernardo; Shu, Chi-Wang Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261 https://doi.org/10.1023/A:1012873910884	journal	September 2001
Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation Habetler, G. J.; Matkowsky, B. J. Journal of Mathematical Physics, Vol. 16, Issue 4 https://doi.org/10.1063/1.522618	journal	April 1975
Diffusion approximation and computation of the critical size Bardos, C.; Santos, R.; Sentis, R. Transactions of the American Mathematical Society, Vol. 284, Issue 2 https://doi.org/10.1090/S0002-9947-1984-0743736-0	journal	February 1984
Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit Guermond, Jean-Luc; Kanschat, Guido SIAM Journal on Numerical Analysis, Vol. 48, Issue 1 https://doi.org/10.1137/090746938	journal	January 2010
Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation Han, Weimin; Huang, Jianguo; Eichholz, Joseph A. SIAM Journal on Scientific Computing, Vol. 32, Issue 2 https://doi.org/10.1137/090767340	journal	January 2010
Positive and Asymptotic Preserving Approximation of the Radiation Transport Equation Guermond, Jean-Luc; Popov, Bojan; Ragusa, Jean SIAM Journal on Numerical Analysis, Vol. 58, Issue 1 https://doi.org/10.1137/19M1260785	journal	January 2020
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo SIAM Journal on Numerical Analysis, Vol. 39, Issue 5 https://doi.org/10.1137/S0036142901384162	journal	January 2002
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations Jin, Shi SIAM Journal on Scientific Computing, Vol. 21, Issue 2 https://doi.org/10.1137/S1064827598334599	journal	January 1999
A Mixed Variational Framework for the Radiative Transfer Equation Egger, Herbert; Schlottbom, Matthias Mathematical Models and Methods in Applied Sciences, Vol. 22, Issue 03 https://doi.org/10.1142/S021820251150014X	journal	March 2012
Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems Adams, Marvin L. Nuclear Science and Engineering, Vol. 137, Issue 3 https://doi.org/10.13182/NSE00-41	journal	March 2001

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97 MATHEMATICS AND COMPUTING
diffusion limit
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radiative transport

Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

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