Two-Step Extended Sampling Method for the Inverse Acoustic Source Problem. (7th February 2020)

• Record Type: Journal Article
• Authors: Sun, Jiyu; Han, Yuhui
• Other Names: Sadarangani Kishin Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-02-07
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/6434607
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Recently, a new method, called the extended sampling method (ESM), was proposed for the inverse scattering problems. Similar to the classical linear sampling method (LSM), the ESM is simple to implement and fast. Compared to the LSM which uses full-aperture scattering data, the ESM only uses the scattering data of one incident wave. In this paper, we generalize the ESM for the inverse acoustic source problems. We show that the indicator function of ESM, which is defined using the approximated solutions of some linear ill-posed integral equations, is small when the support of the source is contained in the sampling disc and is large when the source is outside. This behavior is similar to the ESM for the inverse scattering problem. Numerical examples are presented to show the effectiveness of the method.