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A Systematic Solution Approach for Neutron Transport Problems in Diffuse RegimesA systematic solution approach for the neutron transport equation, based on a least-squares finite-element discretization, is presented. This approach includes the theory for the existence and uniqueness of the analytical as well as of the discrete solution, bounds for the discretization error, and guidance for the development of an efficient multigrid solver for the resulting discrete problem. To guarantee the accuracy of the discrete solution for diffusive regimes, a scaling transformation is applied to the transport operator prior to the discretization. The key result is the proof of the V-ellipticity and continuity of the scaled least-squares bilinear form with constants that are independent of the total cross section and the absorption cross section. For a variety of least-squares finite-element discretizations this leads to error bounds that remain valid in diffusive regimes. Moreover, for problems in slab geometry a full multigrid solver is presented with V(1, 1)-cycle convergence rates approximately equal to 0.1, independent of the size of the total cross section and the absorption cross section.
Document ID
19970006603
Acquisition Source
Langley Research Center
Document Type
Conference Paper
Authors
Manteuffel, T. A.
(Colorado Univ. Boulder, CO United States)
Ressel, K. J.
(Interdisciplinary Project Center for Supercomputing Zurich, Switzerland)
Date Acquired
August 17, 2013
Publication Date
September 1, 1996
Publication Information
Publication: Seventh Copper Mountain Conference on Multigrid Methods
Subject Category
Atomic And Molecular Physics
Accession Number
97N13532
Funding Number(s)
CONTRACT_GRANT: NSF DMS-87-04169
CONTRACT_GRANT: DE-FG03-93ER-25165
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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