TITLE:
Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle
AUTHORS:
Antonio Scalia, Mezhlum A. Sumbatyan
KEYWORDS:
Reconstruction, Global Optimization, Green's Function, Triangular Domain, Boundary Integral
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.3,
March
24,
2011
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.