Inverse scattering problem for a rigid scatterer or a cavity in elastodynamics

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 91; no. 4; pp. 276 - 287
• Main Authors: Gintides, D., Midrinos, L.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.04.2011; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Exact sciences and technology; Integral equations; inverse scattering problems; Linear elasticity; Mathematical analysis; Mathematics; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Sciences and techniques of general use; integral equations; Applied mechanics; Linear elasticity; Applied mathematics; inverse scattering problems; Integral equation; Numerical method; Parameterization; Inverse problem
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201000098

We consider the inverse scattering problem for the shape determination of a rigid scatterer or a cavity in a homogeneous and isotropic elastic medium. Both problems are formulated in R2 for time‐harmonic fields and longitudinal or transversal incident plane waves. Representation of the scattered field as a single‐ or a double‐layer potential, equivalently, leads to a system of two nonlinear integral equations for the density and the parametrization of the boundary. A detailed numerical implementation is presented for computing the corresponding solutions of both systems and numerical reconstructions are given to show the effectiveness of the method. The authors consider the inverse scattering problem for the shape determination of a rigid scatterer or a cavity in a homogeneous and isotropic elastic medium. Both problems are formulated in R2 for time‐harmonic fields and longitudinal or transversal incident plane waves. Representation of the scattered field as a single‐ or a double‐layer potential, equivalently, leads to a system of two nonlinear integral equations for the density and the parametrization of the boundary. A detailed numerical implementation is presented for computing the corresponding solutions of both systems and numerical reconstructions are given to show the effectiveness of the method.