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Transport synthetic acceleration with opposing reflecting boundary conditions

Journal Article:

Abstract

The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission  More>>
Publication Date:
Feb 01, 2000
Product Type:
Journal Article
Reference Number:
EDB-00:007367
Resource Relation:
Journal Name: Nuclear Science and Engineering; Journal Volume: 134; Journal Issue: 2; Other Information: PBD: Feb 2000
Subject:
66 PHYSICS; 22 NUCLEAR REACTOR TECHNOLOGY; BOUNDARY CONDITIONS; NEUTRON TRANSPORT; ITERATIVE METHODS; ALGORITHMS; MATRICES
Sponsoring Organizations:
USDOE; National Science Foundation (NSF)
OSTI ID:
20014326
Research Organizations:
Lawrence Livermore National Lab., CA (US)
Country of Origin:
United States
Language:
English
Contract Number:
AC05-76OR00033; W-7405-ENG-48
Other Identifying Numbers:
Journal ID: ISSN 0029-5639; NSENAO; TRN: US0001056
Submitting Site:
DELTA
Size:
page(s) 159-170
Announcement Date:

Journal Article:

Citation Formats

Zika, M R, and Adams, M L. Transport synthetic acceleration with opposing reflecting boundary conditions. United States: N. p., 2000. Web.
Zika, M R, & Adams, M L. Transport synthetic acceleration with opposing reflecting boundary conditions. United States.
Zika, M R, and Adams, M L. 2000. "Transport synthetic acceleration with opposing reflecting boundary conditions." United States.
@misc{etde_20014326,
title = {Transport synthetic acceleration with opposing reflecting boundary conditions}
author = {Zika, M R, and Adams, M L}
abstractNote = {The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.}
journal = {Nuclear Science and Engineering}
issue = {2}
volume = {134}
journal type = {AC}
place = {United States}
year = {2000}
month = {Feb}
}