Direct and inverse elastic scattering from anisotropic media
- Bao, Gang
- Hu, Guanghui
- Yin, Tao
- Sun, Jiguang
2010 Mathematics Subject Classification
- 35R30 74B05 78A46
- linear elasticity, Lamé system, variational approach, Fréchet derivative, Dirichlet-to-Neumann map, inverse scattering
Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show uniqueness and existence of weak solutions by applying the Fredholm alternative and using properties of the Dirichlet-to-Neumann map in both two and three dimensions. The Fréchet derivative of the near-field solution operator with respect to the scattering interface is derived. As an application, we design a descent algorithm for recovering the interface from the near-field data of one or several incident directions and frequencies. Numerical examples in 2D are demonstrated to show the validity and accuracy of our methods.
- J. Math. Pures Appl., 117 (2018), pp. 263--301.