## Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

## Abstract

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1246339

- Report Number(s):
- LA-UR-14-28681

Journal ID: ISSN 0029-5639

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 181; Journal Issue: 3; Journal ID: ISSN 0029-5639

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Mathematics

### Citation Formats

```
Willert, Jeffrey, Park, H., and Taitano, William. Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering. United States: N. p., 2015.
Web. doi:10.13182/NSE14-131.
```

```
Willert, Jeffrey, Park, H., & Taitano, William. Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering. United States. doi:10.13182/NSE14-131.
```

```
Willert, Jeffrey, Park, H., and Taitano, William. Sun .
"Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering". United States. doi:10.13182/NSE14-131. https://www.osti.gov/servlets/purl/1246339.
```

```
@article{osti_1246339,
```

title = {Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering},

author = {Willert, Jeffrey and Park, H. and Taitano, William},

abstractNote = {High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.},

doi = {10.13182/NSE14-131},

journal = {Nuclear Science and Engineering},

number = 3,

volume = 181,

place = {United States},

year = {2015},

month = {11}

}

Other availability

Cited by: 2 works

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