A Straightforward Updating Criterion for 2-D/3-D Hybrid Discontinuous Galerkin Time-Domain Method Controlling Comparative Error

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 this paper, a novel criterion is proposed. Compared with the traditional one, this new criterion controls comparative error instead of absolute error, thus enhancing accuracy and flexibility. Besides, for the time-adaptive updating algorithm, the proposed criterion is derived directly from the discretized matrix equations of the DGTD method, rendering it straightforward and efficient. Finally, the 2-D/3-D DGTD with the proposed criterion is integrated with the modified nodal analysis technique for the analysis of power-ground plate pairs with decoupling capacitors. The accuracy, flexibility, and efficiency enhancement of the proposed criterion are demonstrated by comparison with commercial software and the traditional method.