A fast iterative method for identifying the radiogenic source for the helium production-diffusion equation. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Zhang, Zhengqiang; Zhang, Yuan-Xiang
• Is Part Of: Applied mathematics in science and engineering. Volume 30:Issue 1(2022)
• Page Start: 521
• Page End: 540
• Publication Date: 2022-01-02
• Subjects: Inverse source problem -- ill-posed problem -- iterative regularization method -- convergence rate -- production-diffusion equation; 11C08 -- 11C99 -- 11S05; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2022.2097224
• Languages: English
• ISSNs: 2769-0911

Abstract

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.