Liu, Lihan; Cui, Xiaoying; Cai, Jingqiu Reciprocity gap method for an interior inverse scattering problem with a Neumann boundary condition. (Chinese. English summary) Zbl 1438.74091 Acta Sci. Nat. Univ. Sunyatseni 58, No. 1, 149-155 (2019). Summary: An interior inverse scattering problem with a Neumann boundary condition is studied by using reciprocity gap method. First, the conclusion that the position and shape of a cavity with a Neumann boundary condition can be uniquely determined by providing measurements of point sources inside the cavity is proven. Next, by following the idea of reciprocity gap method, a numerical algorithm to effectively reconstruct position and shape of an unknown cavity from interior measurements is designed. Finally, some numerical examples to validate the method are presented. MSC: 74J20 Wave scattering in solid mechanics 74J25 Inverse problems for waves in solid mechanics 78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory Keywords:cavity; interior inverse scattering problem; Neumann boundary condition; reciprocity gap method PDFBibTeX XMLCite \textit{L. Liu} et al., Acta Sci. Nat. Univ. Sunyatseni 58, No. 1, 149--155 (2019; Zbl 1438.74091) Full Text: DOI