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Nuclear Science and Engineering Volume 159, 2008 - Issue 2
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Technical Paper

A Functional Monte Carlo Method for k-Eigenvalue Problems

Edward W. LarsenUniversity of MichiganDepartment of Nuclear Engineering and Radiological Sciences Ann Arbor, Michigan 48109-2104
&
Jinan YangUniversity of MichiganDepartment of Nuclear Engineering and Radiological Sciences Ann Arbor, Michigan 48109-2104
Pages 107-126 | Published online: 10 Apr 2017

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Anurag Gupta & R. S. Modak. (2020) Monte Carlo Solution of k-Eigenvalue Problem Using Subspace Iteration Method. Nuclear Science and Engineering 194:2, pages 87-103.
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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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Jeffrey Willert, H. Park & William Taitano. (2015) Using Anderson Acceleration to Accelerate the Convergence of Neutron Transport Calculations with Anisotropic Scattering. Nuclear Science and Engineering 181:3, pages 342-350.
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Jeffrey Willert, H. Park & William Taitano. (2015) Applying Nonlinear Diffusion Acceleration to the Neutron Transport k-Eigenvalue Problem with Anisotropic Scattering. Nuclear Science and Engineering 181:3, pages 351-360.
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Nam Zin Cho, Seungsu Yuk, Han Jong Yoo & Sunghwan Yun. (2013) Overlapping Local/Global Iteration Framework for Whole-Core Transport Solution. Nuclear Science and Engineering 175:3, pages 227-238.
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Ding She, Kan Wang & Ganglin Yu. (2012) Asymptotic Wielandt Method and Superhistory Method for Source Convergence in Monte Carlo Criticality Calculation. Nuclear Science and Engineering 172:2, pages 127-137.
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D. A. Knoll, H. Park & C. Newman. (2011) Acceleration of k-Eigenvalue/Criticality Calculations Using the Jacobian-Free Newton-Krylov Method. Nuclear Science and Engineering 167:2, pages 133-140.
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D. A. Knoll, H. Park & Kord Smith. (2011) Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry. Nuclear Science and Engineering 167:2, pages 122-132.
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Loren Roberts & Dmitriy Y. Anistratov. (2010) Nonlinear Weighted Flux Methods for Particle Transport Problems in Two-Dimensional Cartesian Geometry. Nuclear Science and Engineering 165:2, pages 133-148.
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Abdullah G. Weiss, Pavel V. Tsvetkov, Jason Hearne, Mark L. Kimber, David W. Wootan & Sean M. McDeavitt. (2023) A sensitivity analysis to predict the neutronics behavior of samples irradiated in the VTR rabbit system. Annals of Nuclear Energy 185, pages 109708.
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Jiahao Chen, Jason Hou & Kostadin Ivanov. (2023) A hybrid neutronics method with novel fission diffusion synthetic acceleration for criticality calculations. Nuclear Engineering and Technology 55:4, pages 1428-1438.
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Xiaoyu Guo, Guanbo Wang & Kan Wang. (2023) Convergence characteristics and acceleration of the transient fixed source equation solved by Monte Carlo method. Frontiers in Energy Research 10.
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Ze-Guang Li, Kan Wang, Yu-Chuan Guo & Xiao-Yu Guo. (2021) Forced propagation method for Monte Carlo fission source convergence acceleration in the RMC. Nuclear Science and Techniques 32:3.
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Youqi Zheng, Yunzhao Li & Liangzhi Cao. 2021. Deterministic Numerical Methods for Unstructured-Mesh Neutron Transport Calculation. Deterministic Numerical Methods for Unstructured-Mesh Neutron Transport Calculation 243 270 .
M.R. Omar, J.A. Karim & T.L. Yoon. (2020) An efficient Monte Carlo fission source convergence acceleration strategy adapted from the survival biasing technique. Annals of Nuclear Energy 138, pages 107164.
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Qi Zheng, Wei Shen, Yunzhao Li, Hongchun Wu & Liangzhi Cao. (2019) A deterministic-stochastic energy-hybrid method for neutron-transport calculation. Annals of Nuclear Energy 128, pages 292-299.
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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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Anil K. Prinja. (2015) Effect of spatio-temporal noise in the Eddington factor on the scalar flux. Annals of Nuclear Energy 86, pages 116-122.
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Min Jae Lee, Han Gyu Joo, Deokjung Lee & Kord Smith. (2014) Coarse mesh finite difference formulation for accelerated Monte Carlo eigenvalue calculation. Annals of Nuclear Energy 65, pages 101-113.
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Jeffrey Willert, C.T. Kelley, D.A. Knoll & H. Park. (2013) Scalable Hybrid Deterministic/Monte Carlo Neutronics Simulations in Two Space Dimensions. Scalable Hybrid Deterministic/Monte Carlo Neutronics Simulations in Two Space Dimensions.
Jeffrey Willert, C. T. Kelley, D. A. Knoll & H. Park. (2013) Hybrid Deterministic/Monte Carlo Neutronics. SIAM Journal on Scientific Computing 35:5, pages S62-S83.
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William R. Martin. (2012) CHALLENGES AND PROSPECTS FOR WHOLE-CORE MONTE CARLO ANALYSIS. Nuclear Engineering and Technology 44:2, pages 151-160.
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Sunghwan Yun & Nam Zin Cho. (2010) Acceleration of source convergence in Monte Carlo k-eigenvalue problems via anchoring with a p-CMFD deterministic method. Annals of Nuclear Energy 37:12, pages 1649-1658.
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Anil K. Prinja & Edward W. Larsen. 2010. Handbook of Nuclear Engineering. Handbook of Nuclear Engineering 427 542 .

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