Shape reconstruction for unsteady advection-diffusion problems by domain derivative method. (English) Zbl 1474.65335

Yan, Wenjing; Su, Jian; Jing, Feifei

Abstr. Appl. Anal. 2014, Article ID 673108, 7 p. (2014).

Summary: 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.

MSC:

65M32

Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs

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