Some recent progress on inverse scattering problems within general polyhedral geometry

<p style='text-indent:20px;'>Unique identifiability by finitely many far-field measurements in the inverse scattering theory is a highly challenging fundamental mathematical topic. In this paper, we survey some recent progress on obstacle problems and medium associated with time-harmonic waves within certain polyhedral geometry, where one can establish unique results measurements. Some issues diffraction grating are also considered. Furthermore, geometrical structures of Laplacian transmission eigenfunctions reviewed, which have important applications determination for We discuss techniques methods developed literature. Finally, raise intriguing open future investigation.</p>