瞬变电磁低频近似Maxwell方程的CPML吸收边界及施加方法

A CPML ABC for Maxwell equations with low-frequency approximation in transient electromagnetic modeling

为保证瞬变电磁场晚期信号计算正确,在时域有限差分正演中通常采用低频近似,即将磁场散度方程显式的包含在电磁场迭代方程中,因而H_(z)的求解方式与H_(x)、H_(y)不同,导致常规CPML吸收边界无法施加.本文重新推导了CPML介质中的迭代方程,并将其与常规介质中的迭代方程在形式上进行了统一,提出了一种适用于瞬变电磁低频近似下三维FDTD的CPML边界条件及施加方法.首先采用均匀半空间模型来验证本方法的有效性,发现模拟结果与解析解吻合较好,且模拟用时为采用Dirichlet边界FDTD用时的一半;而且,反射误差实验验证了本文的CPML边界吸收效率较高.之后,模拟了典型的三层模型,发现本方法的模拟结果与线性数字滤波解吻合程度较好.最后采用本方法计算了航空瞬变电磁带地形的复杂模型,实验证明了本文提出的CPML具有广泛的适用性.

To ensure the response accuracy of the transient electromagnetic field at late time,the low-frequency approximation is usually used in the Finite-Difference Time-Domain(FDTD)forward modeling,in which the magnetic field divergence equation is explicitly included in the iterative equation.Therefore,H_(z) is calculated differently from H_(x)and H_(y),causing the conventional Convolution Perfectly Matched Layer(CPML)application method not suitable.In this study,the iterative equation in the CPML medium is re-derived and is formally unified with that in conventional medium.A CPML application method suitable for 3D FDTD of TEM with low-frequency approximation is proposed.Firstly,the uniform half-space model is used to verify the effectiveness of this method.Through comparison,it is found that the numerical result agree with the analytical solution well and the simulation time is half that of the FDTD with Dirichlet boundary.Moreover,the reflection error experiment verifies that the CPML proposed in this paper has good absorption efficiency.After that,a typical three-layer model was tested.The simulation result of this method agree with the linear digital filter solution well.Finally,this method was applied to the airborne TEM forward modeling of the complex terrain model.The tests shown that the proposed CPML has a wide range of applicability.