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

Authors: George Pelekanos; Vassilios Sevroglou

Source: Applicable Analysis, Volume 84, Number 3, March 2005 , pp. 311-328(18)

Publisher: Taylor and Francis Ltd

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

Document Type: Research article

DOI: http://dx.doi.org/10.1080/0003681042000267939

Publication date: 2005-03-01

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