**J. Elschner, G. C. Hsiao, and A. Rathsfeld**

##
Reconstruction of Elastic Obstacles from the Far-Field Data of Scattered
Acoustic Waves

**abstract:**

We consider the inverse problem for an elastic body emerged in a fluid due to an
acoustic wave. The shape of this obstacle is to be reconstructed from the
far-field pattern of the scattered wave. For the numerical solution in the
two-dimensional case, we compare a simple Newton type iteration method with the
Kirsch-Kress algorithm. Our computational tests reveal that the Kirsch-Kress
method converges faster for obstacles with very smooth boundaries. The simple
Newton method, however, is more stable in the case of not so smooth domains and
more robust with respect to measurement errors.

**Mathematics Subject Classification:**
35R30, 76Q05, 35J05

**Key words and phrases:** Acoustic and elastic waves, inverse scattering,
simple Newton iteration, Kirsch-Kress method