最佳一致有理逼近在时间步进算法(MOT)中的应用

The Application of the Best Uniform Rational Approximation in the Marching-on-in Time(MOT)Method

针对时域积分方程算法在求解电磁散射问题时所产生的后时不稳定问题,本文提出了一种基于最佳一致有理逼近理论(Maehly逼近)的时域响应的外推算法。提出以标准差的变化率为标准检测不稳定性,通过早期响应获得一个关于时间变量的有理逼近函数,从而实现响应的外推。通过对不同几何形态散射体的分析,验证了算法的正确性。计算实例表明:通过对不同几何形态散射体的分析,该方法在一定程度上避免了后时不稳定性或者振荡的产生,验证了该方法的正确性和有效性。

Considering the late-time instability occurrs when the time-domain integral equation（TDIE）is used to solve the electromagnetic scattering problems,an extrapolation algorithm based on the best uniform rational approximation（Maehly approximation）is proposed to obtain the time-domain response.A standard based on rate of change of standard deviation theory is proposed to detect the instability.A rational function about time is obtained by the early response,which is used to get the accurate late-time response by extrapolation.Some Numerical examples is given to validate this implementation.