The (F*F) ^1/4-method for the transmission problem in two-dimensional linear elasticity

Abstract

In this article we present an inversion algorithm for the determination of the shape of a two-dimensional penetrable obstacle from knowledge of the elastic field generated by an incident plane compressional and shear wave. In particular, Kirsch's improved variant of the linear sampling method, the so called (F ^* F )^1/4-method is extended to the elastic case. A mathematical analysis that reveals the compactness and normality of the far-field operator is presented. Finally, numerical results are presented showing the robustness of the (F ^* F )^1/4-method with respect to noise.

Keywords:

• Far-field operator
• Normality
• Interior transmission problem
• Sampling method
• Mathematics Subject Classifications: 45A05
• 74B05