基于非结构化网格的人工源频率域三维电磁场数值模拟

摘要

借助COMSOL生成完全非结构化三维网格, 提出了一种可用于求解非均匀介质中可控源电磁法三维问题的有限元数值模拟方法. 为了回避引入场源带来的奇异性, 基于Coulomb规范, 导出了关于耦合二次磁矢量位及电标量位所满足的Maxwell方程组; 形成了Galerkin大型线性代数方程; 鉴于计算机存贮空间及巨大的计算量, 运用预条件复系数Krylov子空间迭代法求解后续形成的大型稀疏对称非正定线性方程组. 主要成果体现在: 笛卡尔坐标系网格生成及优良的局部网格加密; 引入Coulomb规范和适当的边界条件保证矢量位唯一; 采用滑动最小二乘插值获取高精度二次矢量位旋度及标量位梯度. 通过与同类研究结果的比较, 文中所提算法精度得到验证, 且该方法具有良好的通用性.%To generate completely unstructured mesh by COMSOL, a finite-element method can be used to solve controlled-source electromagnetic induction problems in heterogeneous electrically conducting media .In order to avoid singularities introduced by sources, a secondary potential formulation is derived based on the Cou-lomb gauge.Then Galerkin method is applied to differential equations to obtain finite-element linear equations. From the memory and the computational requirements, an efficient pre-conditioner complex Krylov subspace method is used for solving the resulting large sparse linear system of equations.The main aspects of this work in-clude the implementation of unstructured mesh generator with high-quality local mesh refinement.In the Cou-lomb gauge condition in combination with proper boundary conditions the uniqueness of the vector potential is guaranteed, in differentiating the FE-computed potentials using the moving least-squares weighting interpolant scheme.Finally, results are compared with other researches to check the accuracy of the method.The method is general and can also be adapted for CSEM modelling in borehole, marine, and environment geophysics in het-erogeneous media.