  This paper considers the reconstruction of a defect in a two-dimensional
waveguide during non-destructive ultrasonic inspection using a derivative-based
optimization approach. The propagation of the mechanical waves is simulated by
the Scaled Boundary Finite Element Method (SBFEM) that builds on a
semi-analytical approach. The simulated data is then fitted to a given set of
data describing the reflection of a defect to be reconstructed. For this
purpose, we apply an iteratively regularized Gauss-Newton method in combination
with algorithmic differentiation to provide the required derivative information
accurately and efficiently. We present numerical results for three different
kinds of defects, namely a crack, a delamination, and a corrosion. These
examples show that the parameterization of the defect can be reconstructed
efficiently and robustly in the presence of noise.
