Application of linear multifrequencygrey acceleration to preconditioned Krylov iterations for thermal radiation transport
Abstract
The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermallyredistributed scattering through absorptionreemission. In this paper, we investigate the effectiveness and efficiency of LinearMultiFrequencyGrey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a groupdependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a groupindependent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Texas A & M Univ., College Station, TX (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1457277
 Alternate Identifier(s):
 OSTI ID: 1548163
 Report Number(s):
 LAUR1728830
Journal ID: ISSN 00219991; TRN: US1901346
 Grant/Contract Number:
 AC5206NA25396; FG0297ER25308
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 372; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Thermal radiation transport; Preconditioned Krylov Methods; Linear Multifrequency grey acceleration
Citation Formats
Till, Andrew T., Warsa, James S., and Morel, Jim E. Application of linear multifrequencygrey acceleration to preconditioned Krylov iterations for thermal radiation transport. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.06.017.
Till, Andrew T., Warsa, James S., & Morel, Jim E. Application of linear multifrequencygrey acceleration to preconditioned Krylov iterations for thermal radiation transport. United States. doi:10.1016/j.jcp.2018.06.017.
Till, Andrew T., Warsa, James S., and Morel, Jim E. Fri .
"Application of linear multifrequencygrey acceleration to preconditioned Krylov iterations for thermal radiation transport". United States. doi:10.1016/j.jcp.2018.06.017. https://www.osti.gov/servlets/purl/1457277.
@article{osti_1457277,
title = {Application of linear multifrequencygrey acceleration to preconditioned Krylov iterations for thermal radiation transport},
author = {Till, Andrew T. and Warsa, James S. and Morel, Jim E.},
abstractNote = {The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermallyredistributed scattering through absorptionreemission. In this paper, we investigate the effectiveness and efficiency of LinearMultiFrequencyGrey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a groupdependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a groupindependent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.},
doi = {10.1016/j.jcp.2018.06.017},
journal = {Journal of Computational Physics},
number = ,
volume = 372,
place = {United States},
year = {2018},
month = {6}
}