重构外Steklov特征值的交互间隙法

Reconstruction of the exterior Steklov eigenvalues by using a reciprocity gap method

考虑点源入射下含有腔体的介质反散射中出现的外Steklov特征值的重构,提出了一种基于线性积分方程的交互间隙法,利用测量的总场的Cauchy数据来重构特征值,数据测量和入射点源设置在腔体内的不同流形上。给出了该方法的相关理论,特别建立了积分方程近似解的爆破性质与外Steklov特征值之间的联系。数值算例验证了该方法的有效性。

This study is concerned with the reconstruction of the exterior Steklov eigenvalues in inverse scattering for a medium with a cavity due to point sources.A reciprocity gap method based on a linear integral equation is proposed to reconstruct the eigenvalues from the measured Cauchy data of the total field.The measurements and the incident point sources are placed on two different manifolds inside the cavity.The related theory of this method is provided.In particular,the connections between the blow-up property of the approximate solution to the integral equation and the exterior Steklov eigenvalues are built.The viability of this method is verified by the numerical experiments.