FE-BI Formulations for Characteristic Modes

Two types of finite-element boundary-integral (FE-BI) formulations are developed to determine the characteristic modes (CMs) of general composite material objects. The electromagnetic (EM) fields inside the general objects with inhomogeneous anisotropic material are flexibly formulated using the finite-element (FE) formulations, while the EM fields outside the general material objects are accurately described using the boundary-integral (BI) equations defined on the general objects' boundary. The developed FE-BI formulations result in two generalized Hermitian eigenvalue (GHE) equations for the solution of CMs. These two novel FE-BI based formulations provide clear physical explanation for the analysis of the CMs of the general objects. It is found that their corresponding eigenvalues indicate the imaginary part of the complex power of CMs, which are zero at resonance. Simulated results for typical dielectric resonators are presented to clearly demonstrate the accuracy of the proposed FE-BI formulations.