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

• The discrete uniform lattice with defects and sources is considered.
• The explicit formula for amplitudes of waves in the lattice is derived.
• The defect properties are recovered from the information about amplitudes.
• Theoretical modeling of cloaking devices is demonstrated.

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.