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Nuclear Science and Engineering Volume 169, 2011 - Issue 2
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Technical Paper

Multilevel Quasidiffusion Methods for Solving Multigroup Neutron Transport k-Eigenvalue Problems in One-Dimensional Slab Geometry

Dmitriy Y. AnistratovNorth Carolina State University, Department of Nuclear Engineering Raleigh, North Carolina 27695-7909
&
Vladimir Ya. Gol’dinInstitute for Mathematical Modeling, Russian Academy of Sciences Moscow, Russia, 125047
Pages 111-132 | Published online: 10 Apr 2017

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Anthony P. Barbu & Marvin L. Adams. (2023) Convergence Properties of a Linear Diffusion-Acceleration Method for k-Eigenvalue Transport Problems. Nuclear Science and Engineering 197:4, pages 517-533.
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Yunlin Xu, Volkan Seker & Thomas J. Downar. (2020) Quasi-Diffusion Method with 3-D Cross Sections for TREAT Core Analysis. Nuclear Technology 206:6, pages 825-838.
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Luke R. Cornejo, Dmitriy Y. Anistratov & Kord Smith. (2019) Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems. Nuclear Science and Engineering 193:8, pages 803-827.
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James S. Warsa & Dmitriy Y. Anistratov. (2018) Two-Level Transport Methods with Independent Discretization. Journal of Computational and Theoretical Transport 47:4-6, pages 424-450.
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Dmitriy Y. Anistratov & James S. Warsa. (2018) Discontinuous Finite Element Quasi-Diffusion Methods. Nuclear Science and Engineering 191:2, pages 105-120.
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Dmitriy Y. Anistratov. (2013) Multilevel NDA Methods for Solving Multigroup Eigenvalue Neutron Transport Problems. Nuclear Science and Engineering 174:2, pages 150-162.
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Articles from other publishers (13)

Joseph M. Coale & Dmitriy Y. Anistratov. (2023) Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor. Journal of Quantitative Spectroscopy and Radiative Transfer 296, pages 108458.
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Ansar Calloo, Romain Le Tellier & David Couyras. (2023) Anderson acceleration and linear diffusion for accelerating the -eigenvalue problem for the transport equation . Annals of Nuclear Energy 180, pages 109406.
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S. A. Grabovenskaya, V. V. Zaviyalov & A. A. Shestakov. (2022) Two Approaches to Effectively Reduce the Size of Radiative Heat Transfer Problems in Multidimensional Geometry. Mathematical Models and Computer Simulations 14:2, pages 289-296.
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Dmitriy Y. Anistratov. (2021) Nonlinear iterative projection methods with multigrid in photon frequency for thermal radiative transfer. Journal of Computational Physics 444, pages 110568.
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Светлана Александровна Грабовенская, Svetlana Aleksandrovna Grabovenskaya, Вячеслав Викторович Завьялов, Vyacheslav Viktorovich Zav'yalov, Александр Александрович Шестаков & Aleksandr Aleksandrovich Shestakov. (2021) О двух подходах эффективного понижения размерности для задач переноса теплового излучения в многомерной геометрииTwo approaches to effectively reduce the size of radiative heat transfer problems in multidimensional geometry. Математическое моделирование Matematicheskoe modelirovanie 33:9, pages 35-46.
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Pedram Ghassemi & Dmitriy Y. Anistratov. (2020) Multilevel quasidiffusion method with mixed-order time discretization for multigroup thermal radiative transfer problems. Journal of Computational Physics 409, pages 109315.
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Luke R. Cornejo & Dmitriy Y. Anistratov. (2017) The multilevel quasidiffusion method with multigrid in energy for eigenvalue transport problems. Progress in Nuclear Energy 101, pages 401-408.
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Dmitriy Y. Anistratov, Luke R. Cornejo & Jesse P. Jones. (2017) Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems. Journal of Computational Physics 346, pages 278-294.
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Sebastian Schunert, Yaqi Wang, Frederick Gleicher, Javier Ortensi, Benjamin Baker, Vincent Laboure, Congjian Wang, Mark DeHart & Richard Martineau. (2017) A flexible nonlinear diffusion acceleration method for the S transport equations discretized with discontinuous finite elements. Journal of Computational Physics 338, pages 107-136.
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L. Chacón, G. Chen, D.A. Knoll, C. Newman, H. Park, W. Taitano, J.A. Willert & G. Womeldorff. (2017) Multiscale high-order/low-order (HOLO) algorithms and applications. Journal of Computational Physics 330, pages 21-45.
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Nicholas D. Stehle, Dmitriy Y. Anistratov & Marvin L. Adams. (2014) A hybrid transport-diffusion method for 2D transport problems with diffusive subdomains. Journal of Computational Physics 270, pages 325-344.
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Saam Yasseri & Farzad Rahnema. (2014) Hybrid subgroup decomposition method for solving fine-group eigenvalue transport problems. Annals of Nuclear Energy 68, pages 136-145.
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E. N. Aristova & D. F. Baydin. (2013) Implementation of the quasi-diffusion method for calculating the critical parameters of a fast neutron reactor in 3D hexagonal geometry. Mathematical Models and Computer Simulations 5:2, pages 145-155.
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