A fast iterative method for identifying the radiogenic source for the helium production-diffusion equation

References

• Choulli M, Yamamoto M. Conditional stability in determining a heat source. J Inverse Ill-posed Probl. 2004;12(3):233–243.
   Google Scholar
• Hettlich F, Rundell W. Identification of a discontinuous source in the heat equation. Inverse Probl. 2001;17(5):1465.
   Web of Science ®Google Scholar
• Sakamoto K, Yamamoto M. Inverse heat source problem from time distributing overdetermination. Appl Anal. 2009;88(5):735–748.
   Web of Science ®Google Scholar
• Dou FF, Fu CL, Yang F. Identifying an unknown source term in a heat equation. Inverse Probl Sci Eng. 2009;17(7):901–913.
   Web of Science ®Google Scholar
• Hussein MS, Lesnic D, Johansson BT, et al. Identification of a multi-dimensional space-dependent heat source from boundary data. Appl Math Model. 2018;54:202–220.
   Web of Science ®Google Scholar
• Johansson T, Lesnic D. Determination of a spacewise dependent heat source. J Comput Appl Math. 2007;209(1):66–80.
   Web of Science ®Google Scholar
• Xie J, Zou J. Numerical reconstruction of heat fluxes. SIAM J Numer Anal. 2005;43(4):1504–1535.
   Web of Science ®Google Scholar
• Yan L, Fu CL, Dou FF. A computational method for identifying a spacewise-dependent heat source. Int J Numer Method Biomed Eng. 2010;26(5):597–608.
   Web of Science ®Google Scholar
• Yang F, Fu CL. The revised generalized Tikhonov regularization for the inverse time-dependent heat source problem. J Appl Math Comput. 2013;41(1–2):81–98.
   Google Scholar
• Bao G, Dou Y, Ehlers T, et al. Quantifying tectonic and geomorphic interpretations of thermochronometer data with inverse problem theory. Commun Comput Phys. 2011;9(1):129–146.
   Web of Science ®Google Scholar
• Bao G, Ehlers TA, Li P. Radiogenic source identification for the helium production-diffusion equation. Commun Comput Phys. 2013;14(1):1–20.
   Web of Science ®Google Scholar
• Shuster DL, Farley KA. 4he/3he thermochronometry: theory, practice, and potential complications. Rev Mineral Geochem. 2005;58(1):181–203.
   Google Scholar
• Wolf RA, Farley KA, Kass DM. Modeling of the temperature sensitivity of the apatite (ucth)/he thermochronometer. Chem Geol. 1998;148(1):105–114.
   Web of Science ®Google Scholar
• Zhang YX, Yan L. The general a posteriori truncation method and its application to radiogenic source identification for the helium production–diffusion equation. Appl Math Model. 2017;43:126–138.
   Web of Science ®Google Scholar
• Geng X, Cheng H, Liu M. Inverse source problem of heat conduction equation with time-dependent diffusivity on a spherical symmetric domain. Inverse Probl Sci Eng. 2021;29(11):1–16.
   Web of Science ®Google Scholar
• Deng Y, Liu Z. Iteration methods on sideways parabolic equations. Inverse Probl. 2009;25(9):Article ID 095004, 14pp.
   PubMed Web of Science ®Google Scholar
• Wang J-G, Wei T. An iterative method for backward time-fractional diffusion problem. Numer Methods Partial Differ Equ. 2014;30(6):2029–2041.
   Web of Science ®Google Scholar
• Wang JG, Ran YH. An iterative method for an inverse source problem of time-fractional diffusion equation. Inverse Probl Sci Eng. 2018;26(10):1–13.
   Web of Science ®Google Scholar
• Kindermann S. Optimal-order convergence of Nesterov acceleration for linear ill-posed problems. Inverse Probl. 2021;37(6):Article ID 065002, 21pp.
   Web of Science ®Google Scholar
• Neubauer A. On Nesterov acceleration for Landweber iteration of linear ill-posed problems. J Inverse Ill-posed Probl. 2017;25(3):381–390.
   Web of Science ®Google Scholar
• Watson GN. A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press; 1995.
   Google Scholar
• Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer Academic Publishers Group; 1996.
   Google Scholar
• Lai MC, Wang WC. Fast direct solvers for Poisson equation on 2d polar and spherical geometries. Numer Methods Partial Differ Equ: An Int J. 2002;18(1):56–68.
   Web of Science ®Google Scholar
• Schiesser WE, Griffiths GW. A compendium of partial differential equation models: method of lines analysis with matlab. Cambridge: Cambridge University Press; 2009.
   Google Scholar