Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

doi:10.1016/j.jcp.2018.06.017

Title: Application of linear multifrequency-grey 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, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (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 group-dependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a group-independent 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:

^[1]; Warsa, James S. ^[1];

^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Texas A & M Univ., College Station, TX (United States)

Publication Date:: Fri Jun 15 00:00:00 EDT 2018

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1457277

Alternate Identifier(s):: OSTI ID: 1548163

Report Number(s):: LA-UR-17-28830
Journal ID: ISSN 0021-9991; TRN: US1901346

Grant/Contract Number:: AC52-06NA25396; FG02-97ER25308

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 372; Journal ID: ISSN 0021-9991

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 multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport.  United States: N. p., 2018. 
Web.  doi:10.1016/j.jcp.2018.06.017.

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                    Till, Andrew T., Warsa, James S., & Morel, Jim E. Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport.  United States.  https://doi.org/10.1016/j.jcp.2018.06.017

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                    Till, Andrew T., Warsa, James S., and Morel, Jim E. Fri .  
"Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport".  United States.  https://doi.org/10.1016/j.jcp.2018.06.017.  https://www.osti.gov/servlets/purl/1457277.

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@article{osti_1457277,

  title        = {Application of linear multifrequency-grey 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, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (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 group-dependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a group-independent 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         = {Fri Jun 15 00:00:00 EDT 2018},

  month        = {Fri Jun 15 00:00:00 EDT 2018}

}

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Figure 1: Material layout and mesh for the CRASH-like problem. The source is in the shocked argon. Both axes have the same scale.

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