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Abstract and Applied Analysis
Volume 2014, Article ID 673108, 7 pages
Research Article

Shape Reconstruction for Unsteady Advection-Diffusion Problems by Domain Derivative Method

1School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi 710049, China
2Center for Computational Geosciences, Xi'an Jiaotong University, Shaanxi 710049, China

Received 9 August 2013; Revised 23 January 2014; Accepted 27 January 2014; Published 4 March 2014

Academic Editor: Youyu Wang

Copyright © 2014 Wenjing Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the numerical simulation for shape reconstruction of the unsteady advection-diffusion problems. The continuous dependence of the solution on variations of the boundary is established, and the explicit representation of domain derivative of corresponding equations is derived. This allows the investigation of iterative method for the ill-posed problem. By the parametric method, a regularized Gauss-Newton scheme is employed to the shape inverse problem. Numerical examples indicate that the proposed algorithm is feasible and effective for the practical purpose.