WIAS Preprint No. 1479, (2010)

Comparison of numerical methods for the reconstruction of elastic obstacles from the far-field data of scattered acoustic waves



Authors

  • Elschner, Johannes
  • Hsiao, George C.
  • Rathsfeld, Andreas

2010 Mathematics Subject Classification

  • 35R30 76Q05 35J05

Keywords

  • acoustic and elastic waves, inverse scattering, simple Newton iteration, Kirsch-Kress method

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.

Appeared in

  • Mem. Differential Equations Math. Phys., 53 (2011) 63--97 under the new title "Reconstruction of elastic obstacles from the far-field data of scattered acoustic waves"

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