Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle

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.

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.

Keywords

Reconstruction, Global Optimization, Green's Function, Triangular Domain, Boundary Integral

Reconstruction, Global Optimization, Green's Function, Triangular Domain, Boundary Integral

Cite this paper

nullA. 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.

nullA. Scalia and M. Sumbatyan, "Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle,"

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