Numerical solution of a parameter estimation problem arising in Prompt-Gamma Neutron Activation Analysis

References

• Filß P. Specific activity of large-volume sources determined by a collimated external gamma detector. Kerntechnik. 1989;54(3):198–201. doi: 10.1515/kern-1989-540326
   Web of Science ®Google Scholar
• Filß P. Relation between the activity of a high-density waste drum and its gamma count rate measured with an unshielded Ge-detector. Appl Radiat Isot. 1995;48(8):805–812.
   Google Scholar
• Coquard L, Havenith A, Kettler J, et al. Non-destructive material characterization of radioactive waste packages with QUANTOM. In: WM2020 Conference; 2020 March; Phoenix, Arizona.
   Google Scholar
• Coquard L, Hummel J, Nordhardt G, et al. Non-destructive verification of materials in waste packages using QUANTOM. EPJ Nuclear Sci Technol. 2023;9(55 doi: 10.1051/epjn/2022043
   Google Scholar
• Molnar G. Handbook of prompt gamma activation analysis with neutron beams. New York: Springer; 2004. doi: 10.1007/978-0-387-23359-8
   Google Scholar
• Jesser A, Krycki K, Frank M. Partial Cross-Section calculations for PGNAA based on a deterministic neutron transport solver. Nucl Technol. 2022;208(7):1114–1123. doi: 10.1080/00295450.2021.2016018
   Web of Science ®Google Scholar
• Holloway J, Akkurt H. The fixed point formulation for large sample PGNAA – part 1: theory. Nucl Instrum Methods Phys Res A. 2004;522:529–544. doi: 10.1016/j.nima.2003.11.401
   Web of Science ®Google Scholar
• Akkurt H, Holloway J, Smith L. The fixed point formulation for large sample PGNAA – part 2: experimental demonstration. Nucl Instrum Methods Phys Res A. 2004;522:545–557. doi: 10.1016/j.nima.2003.11.400
   Web of Science ®Google Scholar
• Cercignani C. The boltzmann equation and its applications. Springer New York; 1988. doi: 10.1007/978-1-4612-1039-9
   Google Scholar
• Rising ME, Armstrong JC, Bolding SR, et al. MCNP® Code Version 6.3.0 Release Notes. Los Alamos (NM): Los Alamos National Laboratory; 2023. LA-UR-22-33103, Rev. 1.
   Google Scholar
• Gilmore G. Practical Gamma-Ray spectrometry. Wiley; 2008. doi: 10.1002/9780470861981
   Google Scholar
• Seltzer S. Tables of X-Ray mass attenuation coefficients and mass energy-absorption coefficients, NIST Standard Reference Database 126; 1995.
   Google Scholar
• Hinze M, Pinnau R, Ulbrich M, et al. Optimization with PDE constraints. Dordrecht: Springer; 2009. doi: 10.1007/978-1-4020-8839-1
   Google Scholar
• Arridge S, Lionheart W. Nonuniqueness in diffusion-based optical tomography. Opt Lett. 1998;23(11):882–884. doi: 10.1364/OL.23.000882
   PubMed Web of Science ®Google Scholar
• Alnæs M, Blechta J, Hake J, et al. The FEniCS project version 1.5. Archive Numer Softw. 2015;3(100):9–23.
   Google Scholar
• Logg A, Mardal K, Wells G. Automated solution of differential equations by the finite element method. Springer; 2012. doi: 10.1007/978-3-642-23099-8
   Google Scholar
• Geuzaine C, Remacle F. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng. 2009;79(11):1309–1331. doi: 10.1002/nme.v79:11
   Web of Science ®Google Scholar
• Balay S, Abhyankar S, Adams M, et al. PETSc users manual. Argonne National Laboratory; 2020. ANL-95/11 – Revision 3.14.
   Google Scholar
• Falgout R, Meier Yang U. hypre: a library of high performance preconditioners. In: International Conference on Computational Science; 2002 April 21–24; Amsterdam, The Netherlands: Springer.
   Google Scholar
• Saad Y, Schultz M. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. Siam J Sci Stat Comput. 1986;7:856–869. doi: 10.1137/0907058
   Web of Science ®Google Scholar
• Ruge J, Stüben K. Algebraic multigrid. In: McCormick S, editor. Multigrid methods, volume 3 of Frontiers in applied mathematics. SIAM; 1987. p. 73–130. doi: 10.1137/1.9781611971057
   Google Scholar
• Wirgin A. The inverse crime; 2004. doi: 10.48550/arXiv.math-ph/0401050
   Google Scholar
• Zhu C, Byrd RH, Lu P, et al. Algorithm 778: L-BFGS-B: fortran subroutines for large-scale bound-constrained optimization. ACM Trans Math Softw. 1997;23:550–560. doi: 10.1145/279232.279236
   Web of Science ®Google Scholar
• Virtanen P, Gommers R, Oliphant TE, et al. SciPy 1.0: fundamental algorithms for scientific computing in python. Nat Methods. 2020;17:261–272. doi: 10.1038/s41592-019-0686-2
   PubMed Web of Science ®Google Scholar
• Gibson AP, Hebden JC, Arridge SR. Recent advances in diffuse optical imaging. Phys Med Bio. 2005 Feb;50(4):R1. R43doi: 10.1088/0031-9155/50/4/R01
   PubMed Web of Science ®Google Scholar
• Harrach B. On uniqueness in diffuse optical tomography. Inverse Probl. 2009 Apr;25(5):055010. doi: 10.1088/0266-5611/25/5/055010
   Web of Science ®Google Scholar
• Gilbarg D, Trudinger N. Elliptic partial differential equations of second order. Berlin: Springer; 2001. (Classics in mathematics).
   Google Scholar