%0 Journal Article %T Green¡¯s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle %A Antonio Scalia %A Mezhlum A. Sumbatyan %J Applied Mathematics %P 294-302 %@ 2152-7393 %D 2011 %I Scientific Research Publishing %R 10.4236/am.2011.23034 %X 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. %K Reconstruction %K Global Optimization %K Green's Function %K Triangular Domain %K Boundary Integral %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=4388