摘要
基于交替方向隐式差分(ADI-FDTD)法突破了CFL稳定性条件的约束,具有无条件稳定性的特点,而单轴各向异性完全匹配层(UPML)边界条件具有宽频带吸收特性、不需要对电场和磁场进行分裂、迭代公式简单、便于编程的特点,提出基于UPML边界条件的ADI-FDTD三维探地雷达数值模拟算法;通过对三维Maxwell方程进行离散化,推导GPR波的ADI-FDTD及其UPML边界条件2个子时间步的迭代差分公式,以及计算步骤。开发ADI-FDTD三维模拟程序,并对三维复杂GPR模型进行正演模拟,分析该模型的剖面图、切片图及不同时刻6个分量的全波场快照。研究结果表明:由全波场快照可以了解雷达波形在空间中的传播过程及变化规律,有助于对雷达资料进行更可靠、更准确的解释;基于UPML边界条件的ADI-FDTD算法消除了截断边界处的强反射,能对三维复杂的GPR模型进行快速、高效模拟。
Based on the fact that ADI-FDTD can break through the restriction of the CFL stability condition and its unlimited stable,however,UPML boundary condition has the characteristic of absorbing wide frequency and without the necessity for separating electric field from magnetic field,and its simple iterative formula is convenient for compiling program.The GPR numerical simulation arithmetic of ADI-FDTD was put forward based upon UPML boundary condition.Through the discretization of the three-dimension Maxwell equations,two sub-time step iterative finite difference formula of ADI-FDTD and UPML boundary condition of GPR wave were studied,and the compute steps were given separately.Based on this,the responding ADI-FDTD three-dimension simulation program was complied,the program to forward simulate the complex three-dimension GPR model was used,and fence diagram,slice map and the full wave snapshot of six components were obtained.The results show that the regulation of radar wave spreads and changes in the space to guide interpretation of radar data reliably and accurately.The ADI-FDTD algorithm based on the UPML boundary condition can eliminate the strong reflection of truncating boundaries and imitate GPR model＇s reliability and accurately.
出处
《中南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2011年第8期2363-2371,共9页
Journal of Central South University:Science and Technology
基金
国家自然科学基金资助项目(40804027
41074085)
湖南省自然基金重点项目(09JJ3084)
教育部博士点新教师专项科研基金资助项目(200805331082)
关键词
探地雷达
交替方向隐式有限差分法
单轴各向异性完全匹配层
正演
ground penetrating radar
alternating direction iterative finite difference time domain
uniaxial perfectly matched layer
forward simulation
