# Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems

## Abstract

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analytic test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Florida, Gainesville, FL (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1374344

- Alternate Identifier(s):
- OSTI ID: 1402589

- Report Number(s):
- LA-UR-16-27917; LA-UR-15-26505

Journal ID: ISSN 0029-5639; TRN: US1702553

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 185; Journal Issue: 3; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society - Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; boundary perturbations; Roussopoulos; adjoint

### Citation Formats

```
Favorite, Jeffrey A., and Gonzalez, Esteban.
```*Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems*. United States: N. p., 2017.
Web. doi:10.1080/00295639.2016.1277108.

```
Favorite, Jeffrey A., & Gonzalez, Esteban.
```*Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems*. United States. doi:10.1080/00295639.2016.1277108.

```
Favorite, Jeffrey A., and Gonzalez, Esteban. Fri .
"Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems". United States. doi:10.1080/00295639.2016.1277108. https://www.osti.gov/servlets/purl/1374344.
```

```
@article{osti_1374344,
```

title = {Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems},

author = {Favorite, Jeffrey A. and Gonzalez, Esteban},

abstractNote = {Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analytic test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.},

doi = {10.1080/00295639.2016.1277108},

journal = {Nuclear Science and Engineering},

issn = {0029-5639},

number = 3,

volume = 185,

place = {United States},

year = {2017},

month = {3}

}

*Citation information provided by*

Web of Science

Web of Science