大地电磁二维正演中的无网格局部径向基点插值法  

Two-dimensional forward of magnetotelluric using meshless local radial point interpolation method

作　　者：何建设 李俊杰 严家斌[2] 

机构地区：[1]浙江省水利水电勘测设计院,杭州310002 [2]中南大学地球科学与信息物理学院,长沙410083

出　　处：《物探化探计算技术》2015年第3期267-272,共6页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：国家自然科学基金(40874055);湖南省自然科学基金(07JJ5065)

摘　　要：无单元Galerkin法作为较成熟的一种无网格方法,已成功应用于有限元法触及的领域,还解决了如大变形、裂纹扩展及高速冲击等网格方法较难处理的问题,但其最大的缺陷在于系统方程的离散需借助背景网格,因此该方法并非真正意义上的无网格方法。无网格局部径向基点插值法采用子域法构造系统方程,加权残量只要求在局部积分域消除,大大降低了对背景网格的依赖,向真正的无网格迈进了一大步.这里将此方法用于大地电磁二维正演,介绍了该方法的基本原理;从大地电磁二维边值问题出发,利用子域法推导了与之对应的无网格局部弱式系统方程,并用高斯积分将其离散化;论述了局部径向基点插值法较无单元Galerkin法及有限元法的优缺点;最后通过二维模型的计算验证了算法的有效性。Element-free Galerkin method（EFGM）as a relatively mature meshless method not only has been successfully applied in the field of where the finite element method（FEM）used,but also addressed many problems which grid method is difficult to deal with such as large-deformation,fracture and crack growth and high speed impact.Its biggest drawback is that discrete process of system equation involves the background grid generation therefore cannot be called the true sense of meshless method.Subdomain method is used to construct the system equation in meshless local radial point interpolation method（LRPIM）,the weighted residual only be demanded eliminating in local integral domain greatly reduces the dependence on the background grid therefore LRPIM forwards a major step to the true meshless method.This paper devotes two-dimensional magnetotelluric forward by LRPIM and its basic principle is introduced.Weak form equation is derived by subdomain method corresponding to the magnetotelluric two-dimensional boundary value problem then the equation is discrete by gauss integral method.The advantages and disadvantages of LRPIM are analyzed comparing to EFGM and FEM.At last,the validity of the algorithm is verified by two-dimensional model calculations.

关 键 词：局部径向基点插值法 大地电磁 无单元Galerkin法 有限元法 

分 类 号：P631.3[天文地球—地质矿产勘探]