Liu, Xiaodong The factorization method for cavities. (English) Zbl 1292.78014 Inverse Probl. 30, No. 1, Article ID 015006, 18 p. (2014). Summary: The inverse acoustic scattering of point sources by an impenetrable cavity is considered. The scattered fields incited by point source waves are measured on a closed curve inside the cavity. We prove the validity of the factorization method for reconstructing the shape of the cavity. Two explicit examples for circular cavities are given to show the feasibility and effectiveness of the factorization method. Finally, we present some numerical examples in 2D. The reconstructions are as satisfactory as the exterior scattering problems and change only slightly for different measurement curves, different boundary conditions and different wave numbers. Cited in 28 Documents MSC: 78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra Keywords:acoustic scattering; interior eigenvalues; factorization method; cavity; uniqueness PDFBibTeX XMLCite \textit{X. Liu}, Inverse Probl. 30, No. 1, Article ID 015006, 18 p. (2014; Zbl 1292.78014) Full Text: DOI