Consider the Poisson’s equation Ψ″ (x) = ?e v?Ψ + e Ψ?v ? N(x) with the Dirichlet boundary data, and we mainly investigate the inverse problem of determining the unknown function N(x) from a parameter function family. Some uniqueness and stability results in the inverse problem are obtained.
Li-xin FENG~(1+) Yan-cheng QU~2 1 School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China
We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization. For its approximate solution we propose a regularized Newton iteration scheme. For a foundation of Newton type methods we establish the Fr^chet differentiability of solution to the scattering problem with respect to the boundary of the cavity. Some numerical examples of the feasibility of the method are presented.
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.
