由近场谱数据确定阻抗散射体的形状

SPECTRAL DATA OF THE NEAR FIELD FOR LOCATING THE SHAPE OF SCATTERER WITH IMPEDANCE BOUNDARY CONDITION

本文考虑由点源波入射,在获取近场散射数据时具有阻抗边界的散射体的重构问题.区别于N.Grinberg利用Herglotz波函数和单层势的途径,我们利用混合互易关系,得到了远场和近场算子的关系,由该关系和奇异值分解,得到了算子的谱,从而将散射体特征化.数值实验表明,能得到良好的重构.

The paper deals with the reconstruction of the shape of scatterer with impedance boundary considering point source wave incidence and near-field data. It is different from the approach of N.Grinberg and A.Kirsch with Herglotz wave function and single layer potential. We employ mixed reciprocity relation and obtain the relation between near-field and far-field operator. Then, from the singular system of the operator, we obtain its spectral data and characterize the scattering object. Numerical experiments show that it can generate good reconstruction.