阻抗障碍物声散射的反问题

研究了从声散射场的远场分布的信息来再现声阻抗障碍物形状的反问题,建立了求解这类反问题的一种非线性最优化模型,并提出了数值实现该非线性最优化模型的一种两步调整迭代算法.两步过程的应用使在确定未知障碍物形状的非线性最优化步中未知函数的个数达到了最少,而在调整迭代过程中,通过利用前一迭代步所得重构信息,使重构精度得到了相当大的改进.所建立的反演算法的一个特别吸引人的性质是,只需要远场分布的一个Fourier系数即可对未知声阻抗障碍物作几何物形的设别.对大量具有各种几何形状的二维障碍物的数值算例保证了本算法是实用和有效的.

Inverse acoustic impedance obstacle problem

An inverse problem of recovering the shape of a sound-impedance obstacle from a knowledge of the far-field pattern of the acoustic scattering wave is investigated in this paper. A nonlinear optimization scheme is developed for solving the inverse problem, and a two-step adaptive iteration algorithm is proposed for numerically implementing the nonlinear optimization scheme. The use of the two-step procedure results in a large reduction in the number of unknowns in the nonlinear optimization step for determining the shape of the scatterer. The use of the adaptive iteration technique yields a considerable improvement in the quality of the reconstruction by utilizing the knowledge of the reconstruction obtained from the previous iteration step. Numerical experiments for several two-dimensional obstacles having a variety of shapes have been presented showing the practicality and effciency of the inversion approach.