改进的二维三维混合时域不连续伽辽金方法

对高速信号通过电源板时的电源完整性(power integrity, PI)问题进行研究时, 因为电源板中主要模式分布为零阶平行板模式, 可以采用二维简化以提高效率.而对于隔离盘或其它存在纵向不连续性的区域, 则应采用三维算法以保证精度.将两者结合起来的一种二维三维(2D/3D)混合时域不连续伽辽金(discontinuous Galerkin time domain, DGTD)方法可以兼顾精度与效率, 有效地处理这类电磁全波计算问题.其中二维、三维方法采用同一套三棱柱离散的网格, 通过适当设置基函数, 二维区域与二维区域之间可以方便快速地相互转化.随着电磁波的传播, 二维、三维的适用区域是随时间、空间动态变化的.为了准确地捕捉这种动态变化, 文中提出的一种改进的自适应判据, 在每个时间歩对电磁场进行检测, 从而动态地判定二维简化区域.与现有技术的判据控制绝对误差不同, 该方法对相对误差进行控制, 效率高、精度好, 对于不同的结构适应性强.通过数值实验, 与商业软件和全三维(3D)DGTD方法的结果进行了比较和验证.

An improved 2D/3D hybrid discontinuous Galerkin time domain method

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 efficiently. As the electromagnetic wave propagates, the 2D/3D domain decomposition is dependent both on space and time. This work proposes an improved adaptive criterion which monitors the field at every time step, thus updates the 2D/3D domain dynamically. Unlike the state-of-the-art technique controlling absolute error, the proposed criterion controls comparative error. This method is both high efficient and accurate, and flexible for various kinds of structures. Some numerical examples are demonstrated to validate the proposed method. Comparisons with commercial software are also given.