Identifying multipolar acoustic sources by the direct sampling method

ABSTRACT

This paper concerns the direct sampling method for solving the inverse problem of identifying point sources for the Helmholtz equation from far-field data. We develop some novel indicator functions which could determine the locations and intensities of the target multipolar sources with a single wavenumber. Theoretically, the indicating behaviors are rigorously analyzed. Two- and three-dimensional numerical experiments are conducted to illustrate the effectiveness and robustness of the proposed approach.

COMMUNICATED BY:

• Bo Zhang

KEYWORDS:

• Inverse source problem
• Helmholtz equation
• direct sampling method
• single frequency
• far-field

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N21
• 65M32
• 49N45

Acknowledgements

The authors would also like to thank the anonymous referees for their constructive comments and suggestions on improving the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yukun Guo  http://orcid.org/0000-0003-4477-7666

Additional information

Funding

The work of Y. Guo was supported by the National Natural Science Foundation of China (NSF) grants of China under 11601107, 11671111 and 41474102. The work of X. Wang was supported by the National Natural Science Foundation of China (NSF) grants of China under 11671113.