Study On Mixed Discontinuous Galerkin Method For Fractal Equations

Using the accurate and efficient numerical methods to analyze the electromagnetic (EM) scattering properties of complex three-dimensional (3D) objects has been the focus work in the computational electromagnetics. Most of the practical applications of 3D complex targets are usually compounded by the metal and dielectric materials with the fine structure. The traditional volume and surface integral equation (VSIE) analysis of the EM scattering properties of complex 3D objects must use conformal meshes. However, generating a conformal discretization of high definition targets would be tedious and time consumed. Therefore, studying the new VSIE with non-conformal meshes is significant.The discontinuous Galerkin volume and surface integral equation (DG-VSIE) employ h-RWG and h-SWG basis functions for trial and test functions, it can be used to analyze the EM properties of complex 3D objects with non-conformal meshes. Compared with the traditional VSIE, DG-VSIE reduces the difficulty of discretizing 3D complex targets. However, h-RWG and h-SWG basis functions increase the unknowns of VSIE. Therefore, in this paper, the continuous and discontinuous Galerkin volume and surface integral equation (CDG-VSIE) would be studied. Because of combining VSIE and DG-VSIE, the CDG-VSIE is not only to reduce the difficulty of discretizing 3D complex targets, but also to reduce the unknowns of DG-VSIE. Furthermore, the multilevel fast multipole algorithm (MLFMA) is applied in the CDG-VSIE to analyze mixed metal and dielectric objects with electrical larger size.With the further increase of the electrical size of the 3D complex targets, the computer resources consumed by CDG-VSIE are also very large. In this paper, the non-conformal domain decomposition based on CDG-VSIE is studied. As this method has the advantage of independent sub-domain meshes, it would improve the flexibility and practice of the domain decomposition method. At last, the proposed method and MLFMA is combined, which would be further reducing the memory consumption and time consumed. It is important significance for analyzing the EM properties of mixed metal and dielectric objects with electrical larger size.