基于三次插值的大地电磁自适应有限元二维正演模拟

大地电磁(MT)数值模拟中通常使用有限单元法,通过伽辽金(Galerkin)法将微分方程转化为与其等价的泛函形式,对泛函求取极值并在单元上定义插值基函数,得到节点上电磁场值的线性方程组,最终形成大型复对称稀疏矩阵。要达到较高的有限元计算精度,一般采用密集的网格或高次插值的方法,这样做大大的减慢了正演的速度。结合两者的优点利用三次插值和h-型自适应相结合的有限元法来实现MT的正演算法。首先从一个粗网格出发并利用三次插值,通过后验误差估计方法局部加密网格,在计算量较小的情况获得较高的计算精度。这种方法可以针对目标区域和介质分界面发生突变处进行网格加密,不需要全局加密网格。最后通过对国际标准模型COMMEMI-2D1的模拟,分别比较二次插值与三次插值的自适应网格数量和数值模拟结果,证明了三次插值自适应有限元算法的可行性。

Magnetotelluric Two-dimensional forward modeling based on adaptive finite element of cubic interpolation

Finite element methods are commonly used in numerical simulation of MT.Differential equations are transformed into their equivalent functional forms by the Galerkin method,and extracted the extremum for the functional and defined the interpolation basis function on the element.Finally getting the linear equations of the electromagnetic field value at the node,and forming a large complex symmetric sparse matrix.In order to get higher accuracy,the dense grid or high-level interpolation method was generally used.This greatly slow down the speed of the forward.In order to combine the advantages of the two,dually using cubic interpolation and adaptive finite element method to achieve the MT forward algorithm in this paper.First of all,from a coarse grid and use cubic interpolation.The grid is locally encrypted by a posteriori error estimation method,and the calculation is great accuracy when the calculation is simple.This method can encrypt the grid for the target area or at the media interface mutation occurred,rather than encrypt global grid.Finally,by the simulation of the international standard model COMMEMI-2D1 and comparison of the quadratic interpolation with the cubic interpolation used in this paper prove the effectiveness of the proposed algorithm.