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

Abstract

In this paper, we consider an inverse source problem for the helium production-diffusion equation. That is to determine a space-dependent source term in the helium production-diffusion equation from a noisy final data. Since the problem is ill-posed, we propose an effective iterative scheme to deal with the problem. More specifically, we use an acceleration technique to speed up a simple iterative scheme. We also give two kinds of convergence rates by using an a priori and a posteriori regularization parameter choice rule, respectively. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method.

Keywords

• inverse source problem
• ill-posed problem
• iterative regularization method
• convergence rate
• production-diffusion equation