有限元-点插值耦合法大地电磁二维正演模拟

Magnetotelluric two-dimensional forward modelling by finite element-point interpolation coupling method

点插值法(PIM)作为一种典型的全域弱式无网格法,该方法在地质建模时将物性加载到只与坐标有关的高斯积分点上,因此处理复杂模型时较常规网格方法便利,但缺点是计算效率低。将有限元法(FEM)与PIM耦合,形成FE-PIM,用于大地电磁二维正演模拟。利用Galerkin法代入插值法构造的形函数并结合高斯积分公式推导了大地电磁二维无网格化总体矩阵表达式,简述了背景网格积分与边界条件的加载技术,理论模型的数值计算验证了FE-PIM算法的正确性、高效性及其在处理复杂模型上的便利性。

Point interpolation method(PIM)is a typical global weak-form meshfree numerical calculation method.The physical properties of PIM are loaded on Gauss integral points which are only related with coordinates during geological modeling.Therefore,PIM is more convenient while dealing complex model than conventional grid method,but the former computation efficiency is low.We couple FEM and PIM into finite element-point interpolation method(FE-PIM)for magnetotelluric twodimensional forward.Firstly,magnetotelluric two-dimensional discrete system matrix is deduced through substituting the shape function constructed by interpolation method and combining Galerkin method with Gauss integral formula.Then,the principle of background grid integral and the loading technique of boundary conditions are briefly characterized.Finally,the effectiveness and high efficiency of the FE-PIM algorithm and the convenience for complex models are proved by several numerical models.