Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems
Adjointbased firstorder perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate firstorder 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:

^{[1]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Florida, Gainesville, FL (United States)
 Publication Date:
 Report Number(s):
 LAUR1627917; LAUR1526505
Journal ID: ISSN 00295639; TRN: US1702553
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 185; Journal Issue: 3; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; boundary perturbations; Roussopoulos; adjoint
 OSTI Identifier:
 1374344
 Alternate Identifier(s):
 OSTI ID: 1402589
Favorite, Jeffrey A., and Gonzalez, Esteban. Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems. United States: N. p.,
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. 2017.
"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 = {Adjointbased firstorder perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate firstorder 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},
number = 3,
volume = 185,
place = {United States},
year = {2017},
month = {3}
}