基于卷积完全匹配层的非规则网格时域有限元探地雷达数值模拟

复频移完全匹配层(Complex Frequency-Shifted PML,CFS-PML)在长时间时域计算中对凋落波、倏失波具有好的吸收效果,并被广泛应用于时域有限差分模拟中.而本文采用卷积方法将CFS-PML应用于时域有限元求解GPR波动方程的数值模拟中.论文以TM波为例,推导了基于CPML(Convolutional PML)边界的时域有限元GPR波动方程求解公式,采用Newmark-β方法对时间导数进行离散,有效改善了时域有限元GPR数值计算程序的稳定性.并以狭长模型为例,开展了CPML边界中关键参数m、R和κ的选取实验,通过对比反射误差大小确定了综合最优参数组合.相同时刻UPML与CPML波场快照、3个检测点的反射误差比较,说明CPML较UPML具有更好的吸收效果.最后,采用非规则四边形网格对1个复杂GPR模型进行剖分,应用加载CPML边界条件的FETD程序对该模型进行了正演,得到了二维剖面法、宽角法正演GPR剖面图,说明非规则四边形对复杂模型的良好适应性,基于CPML边界条件的FETD可有效减少边界反射误差,能实现对任意复杂不规则模型的正演模拟.

Convolution perfectly matched layer for the Finite-Element Time-Domain method modeling of Ground Penetrating Radar

Complex Frequency-Shifted PML in the long time domain has good absorption effect about litter wave and prosperous lost wave, and is widely used in FDTD simulation. In this paper, the convolution makes CFS-PML apply in the finite element time domain solution numerical of simulation GPR wave equation. In TM wave as an example, in this paper we deduced GPR time domain finite element wave equation solution formula based on CPML (Convolutional PML) boundary, discrete time derivative with Newmark-β method. Then in narrow model as an example, we conducted the select experiment of the key parameters of CPML border m, R and κ, and determine the optimal parameter combination by contrast reflection error by contrast reflection error. By comparison error of UPML and CPML wave field snapshots and reflecting of three detection points, we can conclude CPML has better absorption effect compared with UPML. Finally, the use of irregular quadrilateral mesh makes a complex GPR model subdivision. Application loading CPML boundary conditions FETD program the model was forward. Obtain a two-dimensional cross-sectional method and wide angle method forward GPR cross-sectional view. That explains irregular quadrilateral adaptable for complex models. The boundary conditions FETD on CPML can effectively reduce the boundary reflection error and can achieve positive modeling of arbitrarily complex irregular models.