Linear Sampling and Reciprocity Gap Methods for a Fluid-Solid Interaction Problem in the Near Field

We consider the inverse problem for a fluid-solid interaction problem of locating and determining the shape of the target from measurements of the near field of the fluid pressure at a single frequency. More precisely we assume that the scattered field and its normal derivative are avaible at any receiver on a measurement surface using fields due to source points around the target for a single frequency. To deal with this problem, we have adapted and analyzed the reciprocity gap method as well as the linear sampling method, showing a novel connection among them. These qualitative approaches are validated by using both synthetic and experimental data in [1].