An iterative decomposition method for scatterer reconstruction in \(\mathbb{R}^3\). (English) Zbl 1370.65067
Summary: In this paper we investigate an iterative method to reconstruct the unknown scatter in \(\mathbb{R}^3\), with only the far-field pattern for just one incident wave. We introduce a general boundary condition and prove its Fréchet derivative. Then this iterative method is able to implement without the boundary condition of the scatterer provided. In practical, one can obtain a better reconstruction without a forward solver at each step. The numerical experiments show the feasibility of this method.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 76Q05 | Hydro- and aero-acoustics |
Keywords:
inverse scattering; one incident wave; unknown boundary condition; general boundary condition; three-dimensionalSoftware:
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