Augmented electric field integral equation for dielectric problems in the twilight zone

Summary form only given. Circuit physics prevails in the long-wavelength limit, while wave physics predominates when the structure is comparable to wavelength. The region between circuit physics and wave physics, the twilight zone, defies efficient numerical methods due to the mixed physics involved. We propose to study this regime with the enhancement of the augmented electric field integral equation (A-EFIE). A-EFIE with the well-known Rao-Wilton-Glisson (RWG) basis is proved to be efficient and stable down to very low frequency for perfect electric conductor (PEC). In order to model dielectrics rigorously as well as preserving the low frequency stability, generalized impedance boundary condition (GIBC) operator is introduced to couple with the augmentation technique as in A-EFIE. The GIBC operator is the relationship between the surface electric and magnetic currents (tangential magnetic and electric fields) on an object. It is most generally represented as a full matrix and can be obtained by solving the internal problem using surface integral equation or finite-element methods. Consequently, the GIBC operator is independent of the outside source and the location of the object, and only depends on the material properties and geometrical shape of the object. Therefore, it can be re-used by objects with same shapes and filling materials, greatly reducing the computational costs. Both magnetic and electric currents are significant for dielectrics. But the magnetic current is the “dual” of the electric current, and both of them cannot be represented by RWG basis. Otherwise, the magnetic field integral equation (MFIE) operators will be poorly tested producing ill-conditioned matrices. As a remedy, Buffa-Christiansen/Chen-Wilton basis is used. This basis function is nearly orthogonal to the original RWG basis function and is a linear superposition of RWG basis on a barycentric mesh. As result, the GIBC operator becomes stable and the dielectric proble- is solvable down to very low frequencies. We will also report some numerical results in the presentation.