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

• 作者: Antonio Scalia Mezhlum A. Sumbatyan
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: RECONSTRUCTION Global Optimization Green's Function TRIANGULAR Domain Boundary Integral
• 年，卷（期）: 2011,（3）
• 页码范围: 294-302
• 页数: 9页
• 分类号: O1

摘要

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.