Volume 14, Issue 1
Radiogenic Source Identification for the Helium Production-Diffusion Equation

Gang Bao ,  Todd A. Ehlers and Peijun Li


Commun. Comput. Phys., 14 (2013), pp. 1-20.

Preview Full PDF BiBTex 238 488
  • Abstract

Knowledge of helium diffusion kinetics is critical for materials in which helium measurements are made, particulary for thermochronology. In most cases the helium ages were younger than expected, an observation attributes to diffusive loss of helium and the ejection of high energy alpha particles. Therefore it is important to accurately calculate the distribution of the source term within a sample. In this paper, the prediction of the helium concentrations as function of a spatially variable source term are considered. Both the forward and inverse solutions are presented. Under the assumption of radially symmetric geometry, an analytical solution is deduced based on the eigenfunction expansion. Two regularization methods, the Tikhonov regularization and the spectral cutoff regularization, are considered to obtain the regularized solution. Errorestimates with optimal convergence order areshown betweenthe exact solution and the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed methods.

  • History

Published online: 2014-07

  • Keywords

  • AMS Subject Headings

  • Cited by