Convergence Properties of a Linear Diffusion-Acceleration Method for k-Eigenvalue Transport Problems

References

• M. ADAMS and E. LARSEN, “Fast Iterative Methods for Discrete-Ordinates Particle Transport Calculations,” Prog. Nucl. Energy, 40, 1, 3 (2002); https://doi.org/10.1016/S0149-1970(01)00023-3.
   Web of Science ®Google Scholar
• H. PARK, D. A. KNOLL, and C. K. NEWMAN, “Nonlinear Acceleration of Transport Criticality Problems,” Nucl. Sci. Eng., 172, 1, 52 (2012); https://doi.org/10.13182/NSE11-81.
   Web of Science ®Google Scholar
• K. S. SMITH, “Full-Core, 2-D, LWR Core Calculations with CASMO-4E,” Proc. PHYSOR 2002, Seoul, Korea, 2002.
   Google Scholar
• G. GUNOW, B. FORGET, and K. SMITH, “Full Core 3D Simulation of the BEAVRS Benchmark with OpenMOC,” Ann. Nucl. Energy, 134, 299 (2019); https://doi.org/10.1016/j.anucene.2019.05.050.
   Web of Science ®Google Scholar
• L. R. CORNEJO and D. Y. ANISTRATOV, “Nonlinear Diffusion Acceleration Method with Multigrid in Energy for k-Eigenvalue Neutron Transport Problems,” Nucl. Sci. Eng., 184, 4, 514 (2016); https://doi.org/10.13182/NSE16-78.
   Web of Science ®Google Scholar
• L. R. CORNEJO and D. Y. ANISTRATOV, “The Multilevel Quasidiffusion Method with Multigrid in Energy for Eigenvalue Transport Problems,” Prog. Nucl. Energy, 101, 401 (2017); https://doi.org/10.1016/j.pnucene.2017.05.014.
   Web of Science ®Google Scholar
• R. E. ALCOUFFE, “Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations,” Nucl. Sci. Eng., 64, 2, 344 (1977); https://doi.org/10.13182/NSE77-1.
   Web of Science ®Google Scholar
• D. Y. ANISTRATOV and V. Y. GOL’DIN, “Multilevel Quasidiffusion Methods for Solving Multigroup Neutron Transport k-Eigenvalue Problems in One-Dimensional Slab Geometry,” Nucl. Sci. Eng., 169, 2, 111 (2011); https://doi.org/10.13182/NSE10-64.
   Web of Science ®Google Scholar
• E. LARSEN and B. KELLEY, “CMFD and Coarse-Mesh DSA,” Proc. Int.Conf. PHYSOR 2012, Knoxville, Tennessee, April 15–20, 2012, Vol. 1, p. 728, American Nuclear Society (2012).
   Google Scholar
• K. SMITH, A. HENRY, and R. LORETZ, “The Determination of Homogenized Diffusion Theory Parameters for Coarse Mesh Nodal Analysis,” Proc. Conf. Advances Reactor Physics and Shielding, Sun Valley, Idaho, September 14–17, 1980, p. 294, American Nuclear Society (1980).
   Google Scholar
• D. A. KNOLL, H. PARK, and K. SMITH, “Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry,” Nucl. Sci. Eng., 167, 2, 122 (2011); https://doi.org/10.13182/NSE09-75.
   Web of Science ®Google Scholar
• M. ADAMS, “Synthetically Accelerated Heterogeneous Response-Matrix Method for Linear Transport Calculations,” PhD Thesis, University of Michigan (1986).
   Google Scholar
• M. ADAMS and E. LARSEN, “Synthetic Acceleration of One-Group SN k-Eigenvalue Problems,” Trans. Am. Nucl. Soc., 57 (1988).
   Google Scholar
• I. SUSLOV, “An Algebraic Collapsing Acceleration Method for Acceleration of the Inner (Scattering) Iterations in Long Characteristics Transport Theory,” Proc. Int. Conf. Supercomputing in Nuclear Applications, Paris, France, 2003.
   Google Scholar
• E. MASIELLO and T. ROSSI, “Improvements of the Boundary Projection Acceleration Technique Applied to the Discrete-Ordinates Transport Solver in XYZ Geometries,” Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• Z. PRINCE, Y. WANG, and L. HARBOUR, “A Diffusion Synthetic Acceleration Approach to k-Eigenvalue Neutron Transport Using PJFNK,” Ann. Nucl. Energy, 148, 107714 (2020); https://doi.org/10.1016/j.anucene.2020.107714.
   Web of Science ®Google Scholar
• W. H. REED, “The Effectiveness of Acceleration Techniques for Iterative Methods in Transport Theory,” Nucl. Sci. Eng., 45, 3, 245 (1971); https://doi.org/10.13182/NSE71-A19077.
   Web of Science ®Google Scholar
• E. W. LARSEN, “Unconditionally Stable Diffusion-Synthetic Acceleration Methods for the Slab Geometry Discrete Ordinates Equations. Part I: Theory,” Nucl. Sci. Eng., 82, 1, 47 (1982); https://doi.org/10.13182/NSE82-1.
   Web of Science ®Google Scholar
• E. W. LARSEN, “Diffusion-Synthetic Acceleration Methods for Discrete-Ordinates Problems,” Transp. Theory Stat. Phys., 13, 1–2, 107 (1984); https://doi.org/10.1080/00411458408211656.
   Google Scholar
• M. L. ADAMS and W. R. MARTIN, “Boundary Projection Acceleration: A New Approach to Synthetic Acceleration of Transport Calculations,” Nucl. Sci. Eng., 100, 3, 177 (1988); https://doi.org/10.13182/NSE100-177.
   Web of Science ®Google Scholar
• J. S. WARSA, T. A. WAREING, and J. E. MOREL, “Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities,” Nucl. Sci. Eng., 147, 3, 218 (2004); https://doi.org/10.13182/NSE02-14.
   Web of Science ®Google Scholar
• M. T. CALEF et al., “Nonlinear Krylov Acceleration Applied to a Discrete Ordinates Formulation of the k-Eigenvalue Problem,” J. Comput. Phys., 238, 188 (2013); https://doi.org/10.1016/j.jcp.2012.12.024.
   Web of Science ®Google Scholar
• J. WILLERT, H. PARK, and D. A. KNOLL, “A Comparison of Acceleration Methods for Solving the Neutron Transport k-Eigenvalue Problem,” J. Comput. Phys., 274, 681 (2014); https://doi.org/10.1016/j.jcp.2014.06.044.
   Web of Science ®Google Scholar
• H. G. STONE and M. L. ADAMS, “A Piecewise Linear Finite Element Basis with Application to Particle Transport,” Proc. Topl. Mtg. Nuclear Mathematical and Computational Sciences, Gatlinburg, Tennessee, April 6–11, 2003, p. 6, American Nuclear Society (2003).
   Google Scholar
• T. S. BAILEY et al., “A Piecewise Linear Finite Element Discretization of the Diffusion Equation for Arbitrary Polyhedral Grids,” J. Comput. Phys., 227, 8, 3738 (2008); https://doi.org/10.1016/j.jcp.2007.11.026.
   Web of Science ®Google Scholar
• T. S. BAILEY, “The Piecewise Linear Discontinuous Finite Element Method Applied to the RZ and XYZ Transport Equations,” PhD Thesis, Texas A&M University (2008).
   Google Scholar
• A. P. BARBU and M. L. ADAMS, “Semi-Consistent Diffusion Synthetic Acceleration for Discontinuous Discretizations of Transport Problems,” Proc. Int. Conf. Mathematics, Computational Methods and Reactor Physics, Saratoga Springs, New York, May 3–7, 2009, American Nuclear Society (2009).
   Google Scholar
• E. LEWIS et al., “Benchmark Specification for Deterministic 2-D/3-D MOX Fuel Assembly Transport Calculations Without Spatial Homogenization (C5G7 MOX),” Organisation for Economic Co-operation and Development, Nuclear Energy Agency, Nuclear Science Committee, p. 280 (2001).
   Google Scholar
• C. N. MCGRAW et al., “Accuracy of the Linear Discontinuous Galerkin Method for Reactor Analysis with Resolved Fuel Pins,” Texas A&M University (2015).
   Google Scholar
• A. TILL, “Finite Elements with Discontiguous Support for Energy Discretization in Particle Transport,” PhD Thesis, Texas A&M University (2015).
   Google Scholar