S. Andrieux and A. B. Abda, “Identification of Planar Cracks by Complete Overdetermined Data: Inversion Formulae,” Inverse Problems, Vol. 12, No. 5, 1996, pp. 553-563. doi:10.1088/0266-5611/12/5/002
ABSTRACT: The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.