A New 3-D Nonspurious Discontinuous Galerkin Spectral Element Time-Domain (DG-SETD) Method for Maxwell’s Equations

Abstract

A new discontinuous Galerkin spectral element timedomain (DG-SETD) method for Maxwell's equations based on the field variables E and B is proposed to analyze three-dimensional (3-D) transient electromagnetic phenomena. Compared to the previous SETD method based on the field variables E and H (the 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 EB scheme). Consequently, it can reduce the number of unknowns and computation load. Domain decomposition for the EB scheme SETD method is completed via the DG method. In addition, the 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. Index Terms-Discontinuous Galerkin (DG) method, EB scheme, Maxwell's equations, perfectly matched layer (PML), Riemann solver, spectral element time-domain (SETD) method. I. INTRODUCTION I N computational electromagnetics, finite element timedomain (FETD) method in full-wave simulation has received much attention due to the ability to handle transient and nonlinear phenomena in complex structures [1]-[8]. It has been widely used in IC packaging, smart antennas, electromagnetic compatibility (EMC), bioelectromagnetics, etc. The spectral element time-domain (SETD) method can be viewed as a special case of the FETD method [9]-[13]. While FETD usually employs low-order tetrahedrons to mesh, the SETD method uses hexahedron elements to discretize the computation region, and the interpolation polynomials in the hexahedrons can be either of low order or high order. The SETD method is Manuscript

Efficient Wideband Numerical Simulations for Nanostructures Employing a Drude-Critical Points (DCP) Dispersive Model

“…The expressions and field distributions of the 3D curl- and divergence-conforming basis functions can be found in refs 33 and 35.…”

“…Using Φ and Ψ to test Eqs 5 and 6, respectively, and applying the Riemann solver to treat the numerical flux between adjacent subdomains 33 , the discretized system equation for the i th subdomain can be obtained as:where and are the unknown field vectors for the i th and the j th (local and adjacent) subdomains, respectively. j i is the vector for the impressed current, j D ,1 , j D ,2 and J L , m are the unknown vectors for the polarization currents, and N s is the number of subdomains.…”

“…Third , a hybrid scheme is proposed for the time integration. The second order Runge-Kutta (mid-point) method 33 , 41 is used to update the E and B fields as well as the polarization currents of the Drude model. The Newmark method 42 is chosen to update the polarization currents of the Lorentzian resonances corresponding to the critical points of the band transitions.…”

The Conformal Finite-Difference Time-Domain Simulation of GPR Wave Propagation in Complex Geoelectric Structures

“…The substitution of equations (12), (13), (14), (15) into equations (16), (17), (18) result in the CFDTD formulas expressed as…”

“…Chen et al [12] have derived the analytical wavenumber-(k-) space domain propagators underlying the fractional Laplacian wave equation of the pseudospectral time-domain (PSTD) method; however, PSTD is limited by the limited memory and limited operation speed of a single machine. Tobon et al [13] have proposed a new discontinuous Galerkin spectral element time-domain (DG-SETD) method for Maxwell's equations to analyze three-dimensional (3D) transient electromagnetic phenomena. The SETD method is suitable for the numerical simulation of elastic waves under a complex boundary model, but its meshing is complex [14,15].…”