The Discontinuous Galerkin Time-Domain (DGTD) method has gain great popularity for its capability of obtaining highly accuracy, flexibility, efficiency and parallel-computing. Different basis functions have their own merit in their advantageous applications. In this work, we focus on reseaches of DGTD’s basis functions and their advantageous applications. We firstly designed a nodal high-order based DGTD algorithm and studied its improvement on accuracy. As we known, an ultra-dense-mesh h-refinement will lead to the low-frequency breakdown which has been studied for decades. However, for highorder p-refinement, it is conventionally regarded that the accuracy is only limited by the basis orthogonality. While in…

Power integrity (PI) problem is essential when analyzing high speed signal passing through power ground. The fundamental mode in power ground is the zero-order parallel plate mode, which is capable for 2D simplification. However, in areas around anti-pads and other z-axis discontinuities, 3D algorithm has to be adopted to improve the accuracy. A hybrid 2D／3D discontinuous Galerkin time domain (DGTD) method has advantage on both accuracy and efficiency, thus is effective to cope with such full wave simulations. The 2D and 3D domains share the same triangular prism mesh. With appropriated basis functions, different domains can couple with each other…

In this letter, we develop a prism-based discontinuous Galerkin time-domain (DGTD) algorithm with simplified periodic boundary conditions (PBCs) to analyze infinite doubly periodic frequency selective surfaces (FSS). Most FSS structures contain patterned planar conductive layers and supporting dielectric layers. These layers are very thin compared to the wavelength. Therefore, general tetrahedral discretization of space will unnecessarily increase the number of mesh elements, as well as the number of unknowns. Instead, we propose using prismatic elements, which are more optimal for planar structures, resulting in less unknowns, less memory usage, and higher efficiency. The accuracy of the proposed prism-based DGTD method…

The zeroth-order parallel-plates mode dominates in most parts of the power-ground plates pairs. Domains with such mode distribution can be solved by a simplified 2D algorithm, while only higher-order modes require 3D computation. For DGTD method, different domains can be decoupled with each other by the numerical flux. To distinguish 2D and 3D domains properly, the field distribution has to be known before it is actually solved. This paradox is walked around by a predictive criterion which roughly predicts tn's field distribution based on tn-1's results. Here we introduce an adaptive criterion based on the CFL condition to realize such…

The 2-D/3-D hybrid discontinuous Galerkin time-domain (DGTD) method is efficient to deal with structures that contain elements capable of 2-D simplification. To separate 2-D elements from 3-D ones, a criterion for approximation error manipulation is required. However, in the latest reported technique, this kind of criterion is derived from the causality principle and the Courant–Freidrichs–Lewy constraint, and thus is indirect and inessential to 2-D simplification. As a result, some elements capable of 2-D simplification are unnecessarily flagged as 3-D ones, deteriorating efficiency dramatically. Moreover, controlling absolute error, the traditional criterion is not flexible for structures with complex mode distribution. In…

The 2-D/3-D hybrid discontinuous Galerkin time domain (DGTD) method is efficient to deal with power-ground structures that contain elements capable of 2-D simplification. To generalize the capability of the 2-D/3-D DGTD method to deal with various complex structures in engineering design, a criterion is proposed to differentiate 2-D and 3-D elements adaptively. For domain decomposition criterion at time steptn, the electromagnetic field distribution at the previous time steptn-1is analyzed to identify the zeroth-order parallel-plates mode domain. Compared with the classical static distance criterion, this new adaptive criterion makes the approximation error under control, thus enhancing the stability. The 2-D simplification…