An Adjoint Technique Applied to Slab-Geometry Source-Detector Problems Using the Generalized Spectral Green’s Function Nodal Method

References

• Alcouffe, R. E., E. W. Larsen, W. F. Miller, and B. R. Wienke. 1979. Computational efficiency of numerical methods for the multigroup, discrete-ordinates neutron transport equations: The slab geometry case. Nucl. Sci. Eng. 71 (2):111–127.
   Web of Science ®Google Scholar
• Bal, G., A. B. Davis, and I. Langmore. 2011. A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport. Comput. Phys. 230 (20):7723–7735.
   Google Scholar
• Barros, R. C., and E. W. Larsen. 1990. A numerical method for one-group slab-geometry discrete ordinates problems with no spatial truncation error. Nucl. Sci. Eng. 104:199–208.
   Web of Science ®Google Scholar
• Bell, G. I., and S. Glasstone. 1970. Nuclear reactor theory. New York: Van Nostrand Reinhold.
   Google Scholar
• Curbelo, J. P., O. P. da Silva, and R. C. Barros. 2018. Application of an adjoint technique to one-speed X, Y-geometry source-detector transport problems in the discrete ordinates formulation using a spectral nodal method. Prog. Nucl. Energy 108:445–453.
   Web of Science ®Google Scholar
• Curbelo, J. P., O. P. da Silva, C. R. García, and R. C. Barros. 2017. Shifting strategy in the spectral analysis for the spectral Green’s function nodal method for slab-geometry adjoint transport problems in the discrete ordinates formulation. In Integral methods in science and engineering, eds. C. Constanda, M. Dalla Riva, P. D. Lamberti, and P. Musolino. Vol. 2 of Practical applications. Basel: Birkhäuser, Ch. 20.
   Google Scholar
• de Abreu, M. P. 2004. Mixed singular-regular boundary conditions in multislab radiation transport. Comput. Phys. 197 (1):167–185.
   Google Scholar
• Duderstadt, J. J., and W. R. Martin. 1979. Transport theory. New York: Wiley-Interscience.
   Google Scholar
• Garcia, R. D. M., and C. E. Siewert. 1981. Multigroup transport theory. II. Numerical results. Nucl. Sci. Eng. 78 (4):315–323.
   Web of Science ®Google Scholar
• Garcia, R. D. M., and C. E. Siewert. 1983. Multislab multigroup transport theory with L′th order anisotropic scattering. Comput. Phys. 50:181–192.
   Google Scholar
• Haghighat, A., and J. C. Wagner. 2003. Monte Carlo variance reduction with deterministic importance functions. Prog. Nucl. Energy 42 (1):25–53.
   Web of Science ®Google Scholar
• Lewis, E. E., and W. F. Miller. 1993. Computational methods of neutron transport. La Grange Park, IL: American Nuclear Society.
   Google Scholar
• Menezes, W. A., H. Alves Filho, and R. Barros. 2014. Spectral Green’s function nodal method for multigroup SN problems with anisotropic scattering in slab-geometry non-multiplying media. Ann. Nucl. Energy 64:270–275.
   Web of Science ®Google Scholar
• Militão, D. S., H. Alves, and R. C. Barros. 2012. A numerical method for monoenergetic slab-geometry fixed-source adjoint transport problems in the discrete ordinates formulation with no spatial truncation error. Int. J. Nucl. Energy Sci. Technol. 7 (2):151–165.
   Google Scholar
• Peplow, D. E. 2012. Comparison of hybrid methods for global variance reduction in shielding calculations. Trans. Am. Nucl. Soc. 107:512–515.
   Google Scholar
• Prinja, A. K., and E. W. Larsen. 2010. General principles of neutron transport. In Handbook of nuclear engineering, ed. D. G. Cacuci. New York: Springer Science + Business Media, Ch. 5.
   Google Scholar
• Royston, K., A. Haghighat, W. Walters, C. Yi, and G. E. Sjoden. 2014. Determination of current at a detector window using a hybrid adjoint function methodology. Prog. Nucl. Sci. Technol. 4:528–532.
   Google Scholar
• Silva, D. J. M., H. Alves Filho, and R. C. Barros. 2017. A hybrid spectral nodal method for multigroup X, Y-geometry discrete ordinates eigenvalue problems. Prog. Nucl. Energy 95:33–39.
   Web of Science ®Google Scholar
• Sjoden, G. E. 2002. Deterministic adjoint transport applications for He-3 neutron detector design. Ann. Nucl. Energy 29 (9):1055–1071.
   Web of Science ®Google Scholar
• Sjoden, G. E., and G. M. Ghita. 2009. Transport methods used for homeland security and non-proliferation detection applications: an overview. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2009). Saratoga Springs, NY: American Nuclear Society. ISBN: 978-0-89448-069-0.
   Google Scholar
• Wagner, J. C., and A. Haghighat. 1998. Automated variance reduction of Monte Carlo shielding calculations using the discrete ordinates adjoint functions. Nucl. Sci. Eng. 128 (2):186–208.
   Web of Science ®Google Scholar
• Wagner, J. C., D. E. Peplow, and S. W. Mosher. 2014. FW-CADIS method for global and regional variance reduction of Monte Carlo radiation transport calculations. Nucl. Sci. Eng. 176 (1):37–57.
   Web of Science ®Google Scholar
• Wagner, J. C., D. E. Peplow, S. W. Mosher, and T. M. Evans. 2011. Review of hybrid (deterministic/Monte Carlo) radiation transport methods, codes, and applications at Oak Ridge National Laboratory. Prog. Nucl. Sci. Technol. 2:808–814.
   Google Scholar
• Wu, Z., and H. S. Abdel-Khalik. 2013. Hybrid biasing approaches for global variance reduction. Appl. Radiat. Isot. 72:83–88.
   PubMed Web of Science ®Google Scholar
• Wu, Z., Q. Zhang, and H. S. Abdel-Khalik. 2011. A hybrid variance reduction method based on Gaussian process for core simulation. Trans. Am. Nucl. Soc. 105:872–874.
   Google Scholar