Explicit formula for amplitudes of waves in lattices with defects and sources and its application for defects detection

Abstract

A closed-form expression for the amplitudes of waves passing through the discrete uniform lattice with local defects and local sources is presented. It allows us to recover the defect properties from the available information about the amplitudes of waves. Other applications, such as modeling of cloaking devices, are also considered. The stability of this method is demonstrated by several numerical examples.