## 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:

- 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) (SC-21)

- 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.
```

```
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. doi:10.1016/j.jcp.2018.06.017.
```

```
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. doi:10.1016/j.jcp.2018.06.017. https://www.osti.gov/servlets/purl/1457277.
```

```
@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 = {2018},

month = {6}

}