Recovering the impedance function or shape of elastic obstacle from partial Cauchy data. (English) Zbl 1542.74039
Summary: In this paper, we focus on recovering the impedance function or the boundary shape from a pair of Cauchy data on the known boundary by using an indirect boundary integral equation. This present problem has been divided into two parts. The first part is to solve a Cauchy problem through using an indirect boundary integral equation method combining a regularization technique. Then, the elastic impedance function is given by a point to point method. The second part is to recover the elastic shape by a Newton-type iterative method. The effectiveness of the method has been shown by solving some examples.
MSC:
| 74J25 | Inverse problems for waves in solid mechanics |
| 35N25 | Overdetermined boundary value problems for PDEs and systems of PDEs |
| 35R30 | Inverse problems for PDEs |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
Keywords:
inverse impedance problem; inverse shape problem; Cauchy data; boundary integral equation; Navier equationReferences:
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