Application Of Element-free Galerkin Method In Two-dimensional Magnetotelluric Forward

In the forward of Magnetotelluric,the finite difference method and the finite element method are the methods that most widely used.But these numerical methods basis for grid,the mesh generation of complex geoelectric model is very complicated and the computational accuracy are heavily dependent on the shape and size of the element meshing.To overcome these limitations,the meshless method that an important supplement and development of the mesh method are proposed,it's has important research significance and practical value.This thesis focuses on the magnetotelluric forward modeling based on Element-free Galerkin method.First,from the Maxwell equations of the two-dimensional magnetotelluric field and using the equivalence of variational problems and boundary value problems,we can get the corresponding variational form.Dispersing calculation domain by a series of discrete points and constructing the integral point support domain shape function by moving least square(MLS)method.Based on the principle of Galerkin method,we get the matrix expression of element-free Galerkin method of two-dimensional Magnetotelluric forward.The computational domain is discretized by Gauss integral with background mesh,we can obtain the final matrix expression.Last we give the best relevant parameters by the numerical simulation of several one-dimensional models,for example,the number of Gauss points is 2~3,and the dimensionless support domain size is a=1.1~1.3.Subsequently,several typical one-dimensional model and two-dimensional model are calculated by finite element method and element-free Galerkin method.The effectiveness and superiority in dealing with complex models of the proposed method is verified by comparing the calculated results.Finally,according to the actual situation of the Dong Guashan copper mine,a two-dimensional geological model is designed.The numerical simulation is carried out by using the element-free Galerkin method that presented in this thesis,the calculated results reflect the actual shape of low resistivity orebody.The results also prove that the meshless method is of great significance in the numerical simulation of geophysical electromagnetic field.