×

The factorization method for cracks in inhomogeneous media. (English) Zbl 1499.74055

Summary: We consider the inverse scattering problem of determining the shape and location of a crack surrounded by a known inhomogeneous media. Both the Dirichlet boundary condition and a mixed type boundary conditions are considered. In order to avoid using the background Green function in the inversion process, a reciprocity relationship between the Green function and the solution of an auxiliary scattering problem is proved. Then we focus on extending the factorization method to our inverse shape reconstruction problems by using far field measurements at fixed wave number. We remark that this is done in a non intuitive space for the mixed type boundary condition as we indicate in the sequel.

MSC:

74H75 Inverse problems in dynamical solid mechanics
74G75 Inverse problems in equilibrium solid mechanics
74E05 Inhomogeneity in solid mechanics
74R05 Brittle damage
PDFBibTeX XMLCite
Full Text: DOI