References
- D. A. KNOLL and D. E. KEYES, “Jacobian-Free Newton-Krylov Methods: A Survey of Approaches and Applications,” J. Comput. Phys., 193, 2, 357 (2004); https://doi.org/10.1016/j.jcp.2003.08.010.
- D. F. GILL and Y. Y. AZMY, “Newton’s Method for Solving k-Eigenvalue Problems in Neutron Diffusion Theory,” Nucl. Sci. Eng., 167, 2, 141 (2011); https://doi.org/10.13182/NSE09-98.
- V. S. MAHADEVAN and J. RAGUSA, “Novel Hybrid Scheme to Compute Several Dominant Eigenmodes for Reactor Analysis Problems,” Int. Conf. Physics of Reactors (PHYSOR2008), Interlaken, Switzerland, September 14–19, 2008.
- D. A. KNOLL, H. PARK, and C. NEWMAN, “Acceleration of k-Eigenvalue/Criticality Calculations Using the Jacobian-Free Newton-Krylov Method,” Nucl. Sci. Eng., 167, 2, 133 (2011); https://doi.org/10.13182/NSE09-89.
- D. F. GILL et al., “Newton’s Method for the Computation of k-Eigenvalues in SN Transport Applications,” Nucl. Sci. Eng., 168, 1, 37 (2011); https://doi.org/10.13182/NSE10-01.
- L. ZOU, H. H. ZHAO, and H. B. ZHANG, “Solving Phase Appearance/Disappearance Two-Phase Flow Problems with High Resolution Staggered Grid and Fully Implicit Schemes by the Jacobian-Free Newton-Krylov Method,” Comput. Fluids, 129, 179 (2016); https://doi.org/10.1016/j.compfluid.2016.02.008.
- H. PARK et al., “Jacobian-Free Newton Krylov Discontinuous Galerkin Method and Physics-Based Preconditioning for Nuclear Reactor Simulations,” Int. Conf. Physics of Reactors (PHYSOR2008), Interlaken, Switzerland, September 14–19, 2008.
- P. LUCAS, A. H. V. ZUIJLEN, and H. BIJL, “Fast Unsteady Flow Computations with a Jacobian-Free Newton–Krylov Algorithm,” J. Comput. Phys., 229, 24, 9201 (2010); https://doi.org/10.1016/j.jcp.2010.08.033.
- J. GAN, Y. L. XU, and T. DOWNAR, A Matrix-Free Newton Method for Coupled Neutronics Thermal-Hydraulics Reactor Analysis, Nuclear Mathematical and Computational Sciences, Gatlinburg, Tennessee (2003).
- V. S. MAHADEVAN, “High-Resolution Numerical Methods for Coupled Non-Linear Multi-Physics Simulations with Applications in Reactor Analysis,” PhD Thesis, Texas A&M University (2010).
- D. R. GASTON et al., “Physics-Based Multiscale Coupling for Full Core Nuclear Reactor Simulation,” Ann. Nucl. Energy, 84, 45 (2015); https://doi.org/10.1016/j.anucene.2014.09.060.
- R. D. LAWRENCE, “Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations,” Prog. Nucl. Energy, 17, 271 (1986); https://doi.org/10.1016/0149-1970(86)90034-X.
- K. SMITH. “An Analytical Nodal Method for Solving the Two-Group, Multi-Dimensional, Static and Transient Neutron Diffusion Equations,” PhD Thesis, Massachusetts Institute of Technology (1979).
- Y. Q. WANG, “Nonlinear Diffusion Acceleration for the Multigroup Transport Equation Discretized with SN and Continuous FEM with RattleSnake,” Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C2013), Sun Valley, Idaho, May 5–9, 2013.
- J. D. HALES et al., “Verification of the BISON Fuel Performance Code,” Ann. Nucl. Energy, 71, 81 (2014); https://doi.org/10.1016/j.anucene.2014.03.027.
- R. A. BERRY et al., “RELAP-7 Theory Manual,” INL/EXT–14-31366, Idaho National Laboratory (2016).
- S. C. EISENSTAT and H. F. WALKER, “Choosing the Forcing Terms in an Inexact Newton Method,” SIAM J. Scientific Comput., 17, 1, 16 (1996); https://doi.org/10.1137/0917003.
- J. J. DUDERSTADT and L. J. HAMILTON, Nuclear Reactor Analysis, Wiley, New York (1976).
- Y. L. XU, “A Matrix Free Newton/Krylov Method for Coupling Complex Multi-Physics Subsystems,” PhD Thesis, Purdue University (2004).
- P. N. BROWN and Y. SAAD, “Hybrid Krylov Methods for Nonlinear Systems of Equations,” SIAM J. Sci. Stat. Comput., 11, 3, 450 (1990); https://doi.org/10.1137/0911026.
- “Benchmark Problem Book,” ANL-7416, Suppl. 2, Argonne National Laboratory (1977).