Characteristic mode analysis with discontinuous Galerkin Surface integral equations

Characteristic mode (CM) analysis of multi-scale and complex targets has attracted much attention in computational electromagnetics. However, it is hard to calculate the multi-scale problems in terms of desired accuracy and stability by using conventional methods. What is more, it is a challenging work to generate a good quality mesh for the multi-scale structures including very fine features. In this paper, we present Discontinuous Galerkin (DG) surface integral equations-based theory to analyze the CMs. The multi-scale objects are firstly divided into several subdomains, and we generate the meshes of every parts independently. HRWG basis functions are adopted in our work and the characteristic currents are expanded by HRWG basis functions. In many applications, only characteristic currents with small eigenvalues are desired because they are corresponding to the modes that radiate efficiently and have large modal coefficients. Special singularity extraction schemes are chosen to treat the infinite term in the resulting integral equations since HRWG basis functions are not divergence-conforming and there is divergence operator in electric field integral equation (EFIF) and magnetic field integral equation (MFIE). In DG method, they are no requirements for normal continuity of currents across the contour of between every two subdomains, hence, the proposed method can handle both non-conformal mesh and conformal mesh. Numerical results are presented to validate the propose formulation. This work may offer great flexibility to CM analysis of multi-scale and complex structures.