Multiple Scattering Reconstruction Numerical Algorithms

Mathematical physics inverse problems have a wide range of applications background indaily life and scientific fields, such as, echoes pick watermelon, hear the sound to knowpeople, non-destructive detection, Weather Forecast, CT technology, forensic medicine,archeology and so on. Many practical problems of other research fields can be attributed tomathematical physics inverse problem. this paper studies is the inverse problem of theinverse acoustic scattering problem.While working on the mathematical physics inverse problem, the main difficulty lies inthe ill-posedness of the problem. Inverse acoustic scattering is an important subfield ofmathematical physics inverse problem, so it not only has the ill-posedness of the inverseproblem, but also has a non-linear characteristic. The ill-posedness is mainly behaved in thenumerical calculation, and the continuous dependence of the numerical result on the datainput. This paper studies the reconstruction of multi impenetrable scatters on2-D plane. Thealgorithm of reconstructing the scatter boundary, using far-field pattern of the scatteringwave, is discussed. The achievements are as follows:Firstly, the acoustic forward and backward scattering problems are recommended in theintroduction part. The difference of various problems is the change of the obstacle orboundary conditions, and their basic mathematical model is the Helmloltze equation.Besides, the numerical solution of the forward acoustic wave problem and the usualmethods of the inverse acoustic wave problem are summarized. Secondly, thepre-knowledge for studying acoustic scattering problem are provided in chapter Two. Itincludes the combined potential methods for discrete direct problem. Moreover, an inversenumerical algorithm for reconstructing multi obstacle by an adaptive auxiliary curveselection based on combined potential methods are discussed, which needn’t have to have apre-knowledge of the auxiliary curve in the scatter, compared to Kirsch-Kress algorithms.Finally, the numerical algorithm based on the wave-field decomposition to build multi-scattering field are given. The algorithm uses the single-layer potential to decomposethe scattering field and then takes advantage of the method proposed in Chapter two toreconstruct each scatter. Numerical experiments on two obstacles in three environments.The results showed that the proposed method will have a better representation on twoscatter reconstruction, and has good stability on the noise of the far-field data.