Locating multiple multipolar acoustic sources using the direct sampling method
For inverse source problems in acoustics, this provides a simple and efficient direct method for locating multipolar sources, though it is an incremental improvement over existing sampling methods.
This paper develops direct sampling methods to locate multiple multipolar acoustic sources from boundary measurements for the Helmholtz equation, using novel indicator functions that require only simple integral calculations. Numerical examples demonstrate effectiveness and robustness.
This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods.