On Stability of Discontinuous Galerkin Time-Domain Method for Conductive Medium

In recent years, discontinuous Galerkin time-domain (DGTD) method has found widespread use in computational electromagnetics [1]-[2]. This is due to the fact that it combines the advantages of finite-element and finite-volume methods (FEM and FVM). Just like FEM, it allows for accurate representation of the geometry and uses higher- order basis functions. Like FVM, it uses numerical flux to realize information exchange between discretization elements localizing all spatial operations. This yields a block diagonal mass matrix, where the dimension of each block is equal to the degrees of freedom in each element. The inverse of mass matrix is computed block by block and stored before the time marching starts. Using an explicit integrator to execute the time marching results in a very efficient and compact DGTD solver. Indeed, high-order (explicit) Runge-Kutta (RK) methods are often incorporated with DG frameworks making use of nodal high-order polynomial basis functions to solve Maxwell equations [2].