New, sophisticated methods, such as SAFT (Synthetic Aperture Focusing Technique) pushed the boundaries in Non-Destructive-Testing (NDT), to a level that allows the detection of very small defects, compared to the wavelength of the probe. The use of classic sizing methods, such DGS-method (Distance-Gain-size), is no longer possible when sizing of small defects is desired as they exploit Kirchhof's approximation in order to achieve an easy rule of thumb. Hence, this thesis investigates the scattering of elastic waves at small defects using numerical modeling techniques. The 3D-Elastodynamic-Finite-Integration-Technique (3D-EFIT) is implemented using C# programming language and is used to understand the scattering processes occurring at small defects.

The fundamentals of elastic wave propagation and scattering processes are presented and the discretization of the fundamental equations, used for 3D-EFIT are extensively elaborated. The 3D-EFIT software is used to simulate the scattering of elastic waves at disc shaped re ectors (DSR) and at bottom holes (FBH). The Convolutional Perfectly Matched Layer method is introduced providing an ecient tool for wave attenuation and Auld's Reciprocity Theorem is embedded into the code to compute the echo signal of the scattered, elastic waves. The numerical errors, appearing the simulations is explained and precisely calculated and are kept below are de ned threshold

The simulation results are compared with the DGS-method. Based on the simulation results, an extension to the DGS-method is presented, making it a globally valid tool for sizing. The particular bene t of the numerical treatment of the underlying problem is revealed by proving a strong divergence of the maximum height of the signals between computation results and DGS-theory.