Magnetotelluric Two-dimensional Forward By Weak-form Meshfree Methods

Meshfree method is a kind of important new numerical method as an important supplement and development to the grid method which avoids the mesh generation with the advantages of high precision and simple adaptive analysis has widely applications in the field of computational mechanics in past decade. Meshfree method has a wide types which can mainly divide into three categories of global weak-form, partial weak-form and strong-form. This paper reviews the development of the method and elaborates its principle around meshfree approximation methods and the weighted residual methods and introduces the related parameters like support domain, gauss point and integral domain in meshfree method. Then the global weak-form meshfree method like element-free Galerkin Method(EFGM) and point interpolation method (PIM) and local Petrov-Galerkin method (MLPG) are used for magnetotelluric two-dimensional forward.Firstly, the expression of meshfree global weak-form system matrix is obtained through substituting with shape function constructed by moving least squares (MLS) approximation and point interpolation approximation (PIM) to magnetotelluric two-dimensional variational problem then discretes it by gauss integral with the background grid. The advantages and disadvantages of both approximate methods are discussed and the influence of the support domain dimensionless size and gauss point number to calculation accuracy and efficiency of EFGM is studied. Secondly, the calculation precision of global weak-form meshfree method and finite element method for three layer medium model in the same node distribution is compared, numerical calculation shows that global weak-form meshfree method have the advantages of high precision and convenience of processing complex models. Lastly, in order to reduce its dependence on background grid, the subdomain method is adopted to construct meshfree local Petrov-Galerkin (MLPG) system matrix starting from the magnetotelluric two-dimensional boundary value problem, both the advantages and disadvantages of MLPG comparing to global weak-form meshfree method and finite element method is introduced and the effectiveness of the algorithm is verified by the calculating of two-dimensional model.34pictures,4sheets,80references.