瞬变电磁三维FDTD正演多分辨网格方法

A multi-scale grid scheme in three-dimensional transient electromagnetic modeling using FDTD

瞬变电磁三维时域有限差分(FDTD)正演的网格剖分受最小网格尺寸、时间步长、边界条件、目标尺寸、模型尺寸等的影响,结构化网格一直存在最小网格尺寸受限于异常目标尺寸的矛盾;尽管非均匀网格能够在保证模型尺寸的前提下尽可能的降低网格数量,但由于Yee网格结构的限制,非均匀网格不能无限制的扩大单一方向的尺寸,这是为了避免边界网格区域出现长宽比过大的畸形网格,影响计算精度甚至导致结果发散.在非均匀网格剖分的基础上,本文提出了瞬变电磁三维FDTD正演的多尺度网格方法,即首先使用较大尺寸的粗网格进行第一次剖分,然后在希望加密的区域进行二次剖分,使计算域中包含粗、细两套网格.尽管细网格包含在粗网格内部,但其具有Yee网格的全部属性,因而可以在网格中设置不同的电性参数模拟不同形状的目标.基于Maxwell方程组推导了细网格内电场和磁场的迭代公式,基于泰勒展开给出了设置粗、细网格后产生的内部边界条件,使电磁场的传播在粗、细网格和时间步进上得到统一.采用均匀半空间中包含三维低阻异常的经典模型和三维接触带复杂模型进行精度验证,发现多分辨网格方法计算结果满足精度要求.使用"L"型异常模型计算采用多分辨网格方法和不采用多分辨网格的传统FDTD方法对比计算效率,发现多分辨网格算法能够显著提高计算效率,并能够保证计算精度.

The grid meshing in three-dimensional transient electromagnetic using finite difference time-domain(FDTD)is usually limited by boundary conditions,time step,target size,model size,etc.The smallest grid size is often determined by the abnormal body size,which is a common contradiction for structured grids.The non-uniform grid is an effective method to reduce the number of total grids.However,the aspect ratio cannot be too large according to the limitations of Yee cell to keep the computation accuracy.A multi-scale grid scheme is established based on the non-uniform meshing.A coarse grid is meshed in advance and a fine grid is meshed only in the focused areas.Then the modeling area include at least two types of meshes.The fine grid have all the Yee properties although they are inside of the coarse one.The fine grid can also apply resistivity parameters to form different targets.The electromagnetic iterative formula are derived according to the Maxwell equations.The newly generated inside boundary conditions are given based on the Taylor expansion.Then the coarse and fine grids can be calculated in space and time domain.The typical model with a three dimensional body in a homogeneous half space and a complex conductor at a vertical contact are used for the accuracy verification.The modeling result are in good agreement with that of integral equation method,the normal FDTD method,FEM method and MFVM(Mimetic Finite Volume Method)method.An L shaped model is used to compare the modeling efficiency.The computation time is obviously reduced with the new multi-scale grid scheme.