Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle
Antonio Scalia, Mezhlum A. Sumbatyan
DOI: 10.4236/am.2011.23034   PDF   HTML     5,739 Downloads   9,485 Views   Citations


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.

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A. Scalia and M. Sumbatyan, "Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle," Applied Mathematics, Vol. 2 No. 3, 2011, pp. 294-302. doi: 10.4236/am.2011.23034.

Conflicts of Interest

The authors declare no conflicts of interest.


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