OPTIMIZATION ALGORITHM FOR RECONSTRUCTING INTERFACE CHANGES OF A CONDUCTIVITY INCLUSION FROM MODAL MEASUREMENTS

被引：23

作者：

Ammari, Habib ^{[1
]}

Beretta, Elena ^{[2
]}

Francini, Elisa ^{[3
]}

Kang, Hyeonbae ^{[4
]}

Lim, Mikyoung ^{[5
]}

机构：

[1] Ecole Polytech, CNRS, Ctr Math Appl, UMR 7641, F-91128 Palaiseau, France

[2] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy

[3] Univ Firenze Ulisse Dini, Dipartimento Matemat, I-50134 Florence, Italy

[4] Inha Univ, Dept Math, Inchon 402751, South Korea

[5] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

来源：

MATHEMATICS OF COMPUTATION | 2010年 / 79卷 / 271期

关键词：

Shape reconstruction; vibration analysis; asymptotic expansion; reconstruction algorithm; optimization problem; INHOMOGENEITIES; EIGENVALUES; OPERATORS; FORMULA; DOMAINS;

D O I：

10.1090/S0025-5718-10-02344-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose an original and promising optimization approach for reconstructing interface changes of a conductivity inclusion from measurements of eigenvalues and eigenfunctions associated with the transmission problem for the Laplacian. Based on a rigorous asymptotic analysis, we derive an asymptotic formula for the perturbations in the modal measurements that are due to small changes in the interface of the inclusion. Using fine gradient estimates, we carefully estimate the error term in this asymptotic formula. We then provide a key dual identity which naturally yields to the formulation of the proposed optimization problem. The viability of our reconstruction approach is documented by a variety of numerical results. The resolution limit of our algorithm is also highlighted.

引用

页码：1757 / 1777

页数：21

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