求解时域电场积分方程的不等长时间步步进法

摘要

When using Marching-on-in-Time(MOT) method to solve time domain electric field integral equations,if the time axis of the model is divided by varying steps,the number of the cells needed for calculation will be reduced,but the interpolation will be impossible. To solve this problem,we use inorder traversal of the full binary tree to re-arrange the calcu-lation sequence of time and space,thus fulfill the interpolation.The currents of the linear antenna and the conical-plate electromagnetic pulse simulator are calculated using this Marc-hing-on-in-Time-varying step method.The results are in accordance with those obtained by the MOT method with uniform time steps and the simulation results by the well-known soft-ware CST,but time-consuming is only 41.16% of that by the MOT method with uniform time steps for the current calculation of the conical-plate electromagnetic pulse simulator.At last,the ratio of the number of unknowns in our method to that in the MOT method with u-niform time steps is given out to show our method will save computational cost.%采用时间步进法求解时域电场积分方程时，若时间维度上采用不等长网格进行剖分，能减少未知量个数，但将造成插值无法进行。为解决这一问题，利用满二叉树的中序遍历对求解的时间与空间顺序进行重排，形成了不等长时间步步进法。用该方法对线天线及锥板型电磁脉冲模拟器天线的电流进行了计算，将计算结果与用均匀时间网格模型及成熟软件 CST 计算所得结果进行了对比，三种方法的计算结果一致，证明了该方法的可行性。该方法对锥板型模拟器天线算例的计算时间仅为均匀时间步步进法的41．16％，说明该方法提高了计算效率。最后，给出了该方法与均匀时间步步进法在求解时未知量个数的比值，证明了当空间网格不均匀时，该方法能有效地节约计算量。