Mixed Discretization Scheme Based Discontinuous Galerkin Domain Decomposition Method for Multi-scale Objects

The discontinuous Galerkin (DG)-based domain decomposition method (DDM) for the surface integral equation (SIE) has been proven to be an effective numerical method for modeling multi-scale electromagnetic (EM) problems. This paper aims to further improve the accuracy of the DG-SIE by incorporating a mixed discretization scheme (MDS) built upon Buffa-Christiansen (BC) functions. To this end, we first discuss a special case for constructing BC functions and make it suitable for discretizing the open-surface subdomains generally involved in the DDM framework. In the MDS within the combined field integral equation-based DG method (DG-CFIE), the BC functions act as testing functions for the magnetic field integral equation (MFIE), whereas the Rao-Wilton-Glisson (RWG) basis functions are utilized for discretizing the electric field integral equation (EFIE). Numerical experiments demonstrate that the DG-CFIE employing the new mixed discretization scheme has notably improved accuracy while preserving the previous good properties of flexibility and fast convergence.