Energy methods for non-destructive testing in a two dimensional damaged structure

The article investigates the response to ultrasonic exploration using Helmholtz equations. It concerns non-destructive testing in homogeneous and heterogeneous materials. We suggest an energy invariant for detecting a defect. This quantity is more stable than pointwise values for analyzing the echo of an ultrasonic wave. The model avoids reflection of waves on a part of the boundary in order to simulate infinite structures in one direction. The defect is a circular hole or a slit. Numerical tests are presented in order to illustrate the method.