Direct and inverse elastic scattering from anisotropic media. (English. French summary) Zbl 1397.35094
Summary: Assume that a time-harmonic elastic wave is incident onto a penetrable anisotropic elastic body embedded in a homogeneous isotropic background medium. The scattering problem is reduced to a truncated domain. Uniqueness and existence of weak solutions are proved 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 boundary of the scatterer is derived. As an application, a descent algorithm is designed for recovering the interface from the near-field data of one or several incident directions and frequencies. Numerical examples in 2D are presented to show the validity and accuracy of the algorithm.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J47 | Second-order elliptic systems |
| 65K10 | Numerical optimization and variational techniques |
| 74J20 | Wave scattering in solid mechanics |
Software:
DLMFReferences:
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