Energy Dependent Source Reconstructions via Explicit Formulations of the Adjoint Particles Flux

References

• Badruzzaman, A. 1991. Computational methods in nuclear geophysics. Progress Nuclear Energ. 25 (2–3):265–290.
   Web of Science ®Google Scholar
• Barichello, L. B., and C. E. Siewert. 1999a. A discrete-ordinates solution for a non-grey model with complete frequency redistribution. J. Quantitative Spec. Radiat. Transf. 62 (6):665–675.
   Web of Science ®Google Scholar
• Barichello, L. B., and C. E. Siewert. 1999b. A discrete-ordinates solution for a polarization model with complete frequency redistribution. APJ. 513 (1):370–382.
   Web of Science ®Google Scholar
• Barros, R. C., and E. W. Larsen. 1991. A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error. Transp. Theor. Statistic Phys. 20 (5–6):441–462.
   Google Scholar
• Beck, J., and K. Arnold. 1977. Parameter estimation in engineering and science. New York, NY: John Wiley & Sons.
   Google Scholar
• Bledsoe, K., and J. Favorite. 2007. Using the levenberg-marquardt method for the solution of inverse transport problems with scattering. American Nuclear Society, Proceedings of the Joint International Topical Meeting on Mathematics & Computations and Supercomputing in Nuclear Applications (M & C + SNA), Monterey, CA, April 15–19, pp. 1898–1912.
   Google Scholar
• Dorn, O. 2000. Scattering and absorption transport sensitivity functions for optical tomography. Opt. Express 7 (13):492–506.
   PubMed Web of Science ®Google Scholar
• Duderstadt, J., and W. Martin. 1979. Transport theory. New York, NY: Wiley.
   Google Scholar
• Gao, H., and H. Zhao. 2010. Multilevel bioluminescence tomography based on radiative transfer equation Part 1: L1 regularization. Opt. Express 18 (3):1854–1871.
   PubMed Web of Science ®Google Scholar
• Golub, G. H., and J. Welsch. 1969. Calculation of gauss quadrature rules. Math. Comp. 23 (106):221–230.
   Web of Science ®Google Scholar
• Haltmeier, M., L. Neumann, and S. Rabanser. 2015. Single-stage reconstruction algorithm for quantitative photoacoustic tomography. Inverse Problem. 31 (6):1–24.
   Web of Science ®Google Scholar
• Hykes, J., and Y. Y.Azmy. 2011. Radiation source reconstruction with known geometry and materials using the adjoint. Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C), Rio de Janeiro, Brazil, May 8–12, pp. 1–15.
   Google Scholar
• Kaipio, J., and E. Somersalo. 2005. Statistical and computational inverse problems. New York, NY: Springer.
   Google Scholar
• Kauati, A., A. Silva Neto, and N. Roberty. 2001. A source-detector methodology for the construction and solution of the one-dimensional inverse transport equation. Inverse Problem Eng. 9 (1):45–66.
   Web of Science ®Google Scholar
• Lewis, E., and W. Miller. 1984. Computational methods of neutron transport. New York, NY: John Wiley & Sons.
   Google Scholar
• Miller, K., and W. Charlton. 2007. An inverse transport approach to radiation source location for border security. Proceedings of the 29th Annual Meeting of the European Safeguards Research and Development Association, Aix-en-Provence, France, May 22–24.
   Google Scholar
• Pazinatto, C. B., and L. B. Barichello. 2017. On the use of analytical techniques for source reconstruction problems. International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, Korea, April 16–20.
   Google Scholar
• Pazinatto, C. B., R. C. Barros, and L. B. Barichello. 2016. Analytical adjoint discrete ordinates formulation for monoenergetic slab-geometry source-detector calculations. IJNEST. 10 (2):107–119.
   Google Scholar
• Prinja, A., and E. Larsen. 2010. General principles of neutron transport, chapter 5. In Handbook of nuclear engineering. Vol. 1 of Nuclear engineering fundamentals. New York, NY: Springer.
   Google Scholar
• Scherer, C., J. Prolo Filho, and L. Barichello. 2009. An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics.I. flow problems. Z. Angew. Math. Phys. 60 (1):70–115.
   Web of Science ®Google Scholar
• Siewert, C. E. 1993a. An inverse source problem in radiative transfer. J. Quantitat. Spectro. Rad. Transf. 50 (6):603–609.
   Web of Science ®Google Scholar
• Siewert, C. E. 1993b. A spherical-harmonics method for multi-group or non-gray radiation transport. J. Quantitat. Spectro. Rad. Transf. 49 (2):95–106.
   Web of Science ®Google Scholar
• Siewert, C. E. 2000. A discrete-ordinates solution for multigroup transport theory with upscattering. J. Quantitat. Spectro. Rad. Transf. 64:255–273.
   Web of Science ®Google Scholar
• Somasundaram, E., and T. Palmer. 2016. Application of variational variance reduction for source-detector problems in nuclear non-proliferation. J. Comput. Theor. Transp. 45 (7):554–577.
   Web of Science ®Google Scholar