无单元Galerkin法大地电磁三维正演模拟

无单元Galerkin法(EFGM)作为一种相对成熟的无网格方法,避免了网格剖分,其精度高,适用于复杂电导率分布和复杂边界形状的计算。本文将EFGM用于大地电磁三维正演,详述了三维EFGM形函数的构造过程,从大地电磁三维变分问题出发,利用Galerkin法结合高斯积分公式推导了相应的系统矩阵离散表达式,简述了边界条件的加载技术,研究了支持域尺寸对EFGM三维正演计算精度的影响,最后通过数值计算验证了EFGM三维算法的正确性。

Three-dimensional forward modeling of magnetotellurism using the element-free Galerkin method

The element-free Galerkin method (EFGM) is a relatively mature high-precision mesh-free method which avoids the mesh generation and has the advantages in dealing with complex conductivity distribution and geometrical boundaries. This work applies the EFGM to three-dimensional forward modeling of magnetotellurism (MT). We introduce the shape function constructing process of three-dimensional EFGM and then deduce the discrete system matrix expression corresponding to the three-dimensional variational problem of MT by combining the Galerkin method and the Gauss integral formula. Then, the approach of assigning boundary conditions is briefly described. Finally, the effect of support domain size on the solution accuracy is studied and the correctness of three-dimensional EFGM is verified by numerical calculations of several models.