Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Co...Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer （PML） absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution（RC） method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced.展开更多
The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) appr...The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.展开更多
基于各向异性介质中的时域有限差分(Finite-Difference Time-Domain,FDTD)方法及近似完全匹配层(Nearly Perfect Match Layer,NPML)原理,提出一种截断各向异性介质的修正的NPML吸收边界条件.通过对Maxwell旋度方程中的空间偏导数进行坐...基于各向异性介质中的时域有限差分(Finite-Difference Time-Domain,FDTD)方法及近似完全匹配层(Nearly Perfect Match Layer,NPML)原理,提出一种截断各向异性介质的修正的NPML吸收边界条件.通过对Maxwell旋度方程中的空间偏导数进行坐标拉伸并结合空间插值方法,推导出易于在FDTD方法中实现的吸收边界公式.计算了电偶极子辐射场的反射误差,验证了这种吸收边界截断二维各向异性介质的有效性.三维算例中数值模拟了时谐场的相位分布,以及不同网格NPML吸收层随时间变化的反射误差.数值结果表明NPML吸收边界能有效吸收各向异性介质中的电磁波.展开更多
为衰减地质雷达数值模拟时因截断区域厚度或者参数影响产生的倏逝波,提出了一种利用复频移完美匹配层(complex frequency shifted perfectly matched layer,CFS-PML)作为吸收边界,并结合频域高阶有限元算法(higher order finite element...为衰减地质雷达数值模拟时因截断区域厚度或者参数影响产生的倏逝波,提出了一种利用复频移完美匹配层(complex frequency shifted perfectly matched layer,CFS-PML)作为吸收边界,并结合频域高阶有限元算法(higher order finite element method,HO-FEM)求解电磁总场分量分布情况的新方法.该方法改善了截断域介质本构张量矩阵的特性,利用矩阵频移参量α吸收倏逝波,提高掠射角处吸收性能.数值实验结果表明,与传统PML相比,结合CFS-PML的HO-FEM方法精度得到明显提高,反射误差额外降低10~30 dB,节省了17%~30%的计算时间.此外,该方法能应用于复杂地质结构模型的电磁总场计算,为地质雷达数值模拟提供了一种新的方法.展开更多
文摘Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer （PML） absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution（RC） method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced.
基金Project(41174061) supported by the National Natural Science Foundation of ChinaProject(2011QNZT011) supported by the Free Exploration Program of Central South University,China
文摘The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.
文摘基于各向异性介质中的时域有限差分(Finite-Difference Time-Domain,FDTD)方法及近似完全匹配层(Nearly Perfect Match Layer,NPML)原理,提出一种截断各向异性介质的修正的NPML吸收边界条件.通过对Maxwell旋度方程中的空间偏导数进行坐标拉伸并结合空间插值方法,推导出易于在FDTD方法中实现的吸收边界公式.计算了电偶极子辐射场的反射误差,验证了这种吸收边界截断二维各向异性介质的有效性.三维算例中数值模拟了时谐场的相位分布,以及不同网格NPML吸收层随时间变化的反射误差.数值结果表明NPML吸收边界能有效吸收各向异性介质中的电磁波.
文摘为衰减地质雷达数值模拟时因截断区域厚度或者参数影响产生的倏逝波,提出了一种利用复频移完美匹配层(complex frequency shifted perfectly matched layer,CFS-PML)作为吸收边界,并结合频域高阶有限元算法(higher order finite element method,HO-FEM)求解电磁总场分量分布情况的新方法.该方法改善了截断域介质本构张量矩阵的特性,利用矩阵频移参量α吸收倏逝波,提高掠射角处吸收性能.数值实验结果表明,与传统PML相比,结合CFS-PML的HO-FEM方法精度得到明显提高,反射误差额外降低10~30 dB,节省了17%~30%的计算时间.此外,该方法能应用于复杂地质结构模型的电磁总场计算,为地质雷达数值模拟提供了一种新的方法.
