A new 3-D nonspurious discontinuous galerkin spectral element time-domain (DG-SETD) Method for Maxwell's Equations

A new discontinuous Galerkin spectral element time-domain (DG-SETD) method for Maxwell's equations based on the field variables \mathbf{E} and \mathbf{B} is proposed to analyze three-dimensional (3-D) transient electromagnetic phenomena. Compared to the previous SETD method based on the field variables \mathbf{E} and \mathbf{H} (the \mathbf{EH} scheme), in which different orders of interpolation polynomials for electric and magnetic field intensities are required, the newly proposed method can eliminate spurious modes using basis functions with the same order interpolation for electric field intensity and magnetic flux density (the \mathbf{EB} scheme). Consequently, it can reduce the number of unknowns and computation load. Domain decomposition for the \mathbf{EB} scheme SETD method is completed via the DG method. In addition, the \mathbf{EB} scheme SETD method is extended to the well-posed time-domain perfectly matched layer (PML) to truncate the computation domain when solving open-region problems. The effectiveness and advantages of the new DG-SETD method are validated by eigenvalue analysis and numerical results.