论文详情
作为网格法数值计算的重要补充和发展，无网格法(meshfree)是近十多年来兴起的一类数值计算新方法。点插值法(point interpolation method，PIM)是一种简单高效的无网格方法，克服了有限元法计算复杂模型时网格生成困难的缺陷，在计算力学领域取得了良好的应用效果。将无网格点插值法(MPIM)应用于大地电磁二维正演数值模拟，介绍了点插值法的基本原理，给出了大地电磁二维变分问题的无网格化求解过程。多个二维理论模型的无网格点插值法(MPIM)、无单元Galerkin法(element-free Galerkin method，EFGM)和有限元法(finite element method，FEM)正演计算结果的对比分析表明:无网格点插值法适用于大地电磁正演，其计算精度较高，较有限元法更便于处理复杂模型;无网格点插值法的精度与无单元Galerkin法相当，但其计算效率更高。
As an important supplement and development of mesh numerical calculation,meshfree method is a kind of new numerical algorithm in last decade.Meshfree point interpolation method,as a simple and efficient meshfree method,avoids the mesh generation relative to finite element method and has obtained good results in the field of computational mechanics.This paper devotes meshfree point interpolation method to magnetotelluric two-dimensional forward numerical modeling,and presents the basic principle of meshfree point interpolation method and solving process of magnetotelluric two-dimensional variational problem.Forward results of two-dimensional theoretical models solved by meshfree point interpolation method,element-free galerkin method and finite element method reveal that meshfree point interpolation method for magnetotelluric forward problem is more accurate and is suitable for complex models referring to the conventional finite element method.Meanwhile,meshfree point exploration method has the same accuracy with the element-free Galerkin method,but the former method has higher computation efficiency.