系数优化在改善时间步进算法稳定性中的应用

Application of coefficient optimization in improving the stability of marching-on-in-time scheme

隐式时间步进算法在求解二维物体的散射时,随着时间的推移,也会出现后时不稳定性的问题。文章在先五步后三步平均公式的基础上利用误差公式对系数进行筛选,改善了原公式在隐式时间步进算法中计算二维物体时产生的后时震荡情况;采用基于时域电场积分方程的隐式时间步进算法,分别计算了TM高斯脉冲入射到无限长导体圆柱和导体方柱时的导体表面感应电流。数值计算结果表明所提出的方案有效地改善了后时不稳定的发生,提高了后时的稳定性。

When using the implicit marching-on-in-time（IMOT） scheme to solve the scattering of two-dimensional conducting objects,the later-time instability of the scheme may arise.In this paper,the error formulation is used to optimize the twice-averaging scheme＇s coefficient to restrain the two-dimensional conducting objects＇ later-time oscillation produced by the implicit marching-on-in-time scheme.The induced current of an infinite circular cylinder and an infinite square cylinder illuminated by a TM Gaussian pulse is calculated respectively by using the implicit marching-on-in-time scheme based on time domain electric field integral equation.Numerical results show that the proposed method can effectively restrain the later-time oscillation and improve the later-time stability.