为了提高腔体器件电磁特性的计算效率,基于压缩感知理论,提出了一种时域不连续伽略金快速求解方法。该方法采用节点基函数和蛙跳策略对麦克斯韦方程进行时空离散处理,并在电磁场迭代更新的初始阶段,采用传统方法对区域内的所有单元进行循环计算。当电磁波布满整个区域后,将所有单元视为整体进行全域求解。首先,针对全域质量矩阵,按行进行随机抽取以构建欠定方程;其次,将少量的前时间步结果作为先验知识,以构造待求场值的稀疏变换;最后,利用恢复算法求解欠定方程,从而实现腔体器件电磁特性的快速分析。

A novel discontinuous Galerkin time domain (DGTD) method based on compressive sensing (CS) is proposed to accelerate the analysis of electromagnetic characteristics of cavity devices. In the method, a nodal basis function and a leapfrog scheme are used for the spatial and time discretization of Maxwell equations. Meanwhile, all elements in the computation domain are updated individually by applying the conventional method at the initial stage for electromagnetic field updating. When the electromagnetic wave covers the whole domain, all elements are updated as a whole and a global solution is conducted. First, the underdetermined equations are established by randomly extracting rows from the global mass matrix. Second, the results after a few previous time steps are taken as the prior knowledge to construct a sparse transform. Finally, the underdetermined equations are solved by the recovery algorithms to realize the fast analysis of electromagnetic characteristics of cavity devices.