2-D Electromagnetic Scattering and Inverse Scattering From Anisotropic Objects Under TE Illumination Solved by the Hybrid SIM/SEM

This article presents an efficient hybrid solver based on the spectral-integral method (SIM) and the spectral element method (SEM) which is used to solve both the electromagnetic (EM) scattering and inverse scattering by two-dimensional (2-D) anisotropic objects when the excitation source is transverse electric ( ${\mathrm{TE}}_{{z}}$ )-polarized. The scalar Helmholtz equation describing the magnetic field variation inside the anisotropic region is discretized and solved by SEM and the corresponding computational domain is truncated by a smooth elliptical surface on which SIM is implemented to fulfill the radiation boundary condition (RBC). The scattered EM fields at the receiver array are directly computed by multiplying the spectral-domain solution of the EM fields on the elliptical boundary and the spectral-domain radiation matrix. In the inverse scattering, the sensitivity matrix is constructed by multiplying the adjoint solution of magnetic fields by the first-order derivatives of the system stiffness matrix with respect to anisotropic model parameters inside the inversion domain. Meanwhile, in each iteration, the sensitivity matrix is synchronously updated based on the solution of the forward solver in the last iteration step. Numerical experiments are carried out to show the computation efficiency and correctness of both the scattering and inverse scattering solvers based on the hybrid SIM/SEM.