Discontinuous Galerkin spectral elemen/finite element time domain (DGSE/FETD) method for anisotropic medium

Time domain methods, such as spectral element time domain (SETD) and finite element time domain (FETD) methods have potentials in solving transient and nonlinear problems. SETD method is suitable for the space with only coarse structures. Because large elements in SETD will not bring large geometric error. However, the high-order hexahedrons in SETD method can achieve good accuracy with low spatial sampling density. While tetrahedrons in finite element time domain (FETD) method can seize the detailed geometry information of the fine structures in the computational region, but the low-order elements in FETD is not high efficient as SETD in DoFs. Thus a hybrid of them via discontinuous Galerkin (DG) method can inherit the advantages of both methods. Riemann Solver is used to deal with the energy communication between adjacent subdomains.