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无网格法形函数构造不依赖预定义的单元,具有计算精度高、处理复杂模型便利等优点。本文介绍了无单元Galerkin法(EFGM)、点插值法(PIM)与径向基点插值法(RPIM)三种全域弱式无网格法的近似原理及特点;以二维泊松方程为例研究了支持域无量纲尺寸、场节点与背景网格设置对无网格法计算精度的影响。将RPIM与EFGM应用于频率域线源二维正演,给出了RPIM形状参数的推荐值;分析了均匀介质模型大地电磁(MT)二维正演无网格法边界条件直接加载与罚函数法加载的精度差异,结合PIM与RPIM边界条件加载便利及EFGM计算复杂模型精度高的优势,提出了EFG-PIM及EFGRPIM耦合算法,数值计算结果验证了耦合算法的有效性。研究发现:无网格法及其耦合方法适用于电磁法数值模拟;支持域无量纲尺寸取1.0时无网格法精度与效率高,场节点与背景网格重合时计算效果佳;泊松方程求解PIM及RPIM精度较EFGM低,计算均匀介质MT响应精度较EFGM高;RPIM改善了PIM计算涉及的奇异性问题,对应支持域无量纲尺寸选择空间大。
Meshless shape function does not depend on the predefined unit structure, with the advantages of high computational accuracy, handling complex models and so on. This paper introduces the approximate principles and characteristics of the three global weak meshless methods with element free Galerkin method (EFGM), point interpolation (PIM) and radial basis point interpolation (RPIM). Taking the two-dimensional Poisson equation as an example, The support dimensionless dimension, field node and background mesh setting have influence on the computational accuracy of meshless method. The RPIM and EFGM are applied to two-dimensional forward modeling of frequency domain source, and the recommended values of RPIM shape parameters are given. The direct loading and penalty function of two dimensional forward meshless meshless boundary conditions for homogeneous medium model MT According to the difference of precision of method loading, the EFG-PIM and EFGRPIM coupling algorithm is proposed based on the advantage of convenient loading of boundary conditions between PIM and RPIM and the high precision of EFGM calculation. The numerical results show the effectiveness of the coupling algorithm. The results show that meshless method and its coupling method are suitable for the numerical simulation of electromagnetic method. Meshless method with dimensionless dimension of support domain has high precision and efficiency, and the calculation result is good when field node and background mesh overlap. Poisson equation The accuracy of solving PIM and RPIM is lower than that of EFGM, and the accuracy of MT for calculating uniform medium is higher than that of EFGM. RPIM improves the singularity problem involved in PIM calculation, and corresponds to a large choice of dimensionless size for support domain.