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Three-dimensional complex variable element-free Galerkin method

机译：三维无复变元Galerkin方法

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摘要

The complex variable element-free Galerkin (CVEFG) method is an efficient meshless Galerkin method that uses the complex variable moving least squares (CVMLS) approximation to form shape functions. In the past, applications of the CVMLS approximation and the CVEFG method are confined to 2D problems. This paper is devoted to 3D problems. Computational formulas and theoretical analysis of the CVMLS approximation on 3D domains are developed. The approximation of a 3D function is formed with 2D basis functions. Compared with the moving least squares approximation, the CVMLS approximation involves fewer coefficients and thus consumes less computing times. Formulations and error analysis of the CVEFG method to 3D elliptic problems and 3D wave equations are provided. Numerical examples are given to verify the convergence and accuracy of the method. Numerical results reveal that the CVEFG method has better accuracy and higher computational efficiency than other methods such as the element-free Galerkin method. (C) 2018 Elsevier Inc. All rights reserved.
机译：无复变元Galerkin（CVEFG）方法是一种有效的无网格Galerkin方法，它使用复变最小二乘（CVMLS）逼近来形成形状函数。过去，CVMLS近似和CVEFG方法的应用仅限于二维问题。本文致力于3D问题。提出了在3D域上CVMLS近似的计算公式和理论分析。 3D函数的近似值由2D基函数形成。与移动最小二乘近似相比，CVMLS近似包含较少的系数，因此消耗的计算时间更少。提供了针对3D椭圆问题和3D波动方程的CVEFG方法的公式化和误差分析。数值算例验证了该方法的收敛性和准确性。数值结果表明，CVEFG方法比无元素Galerkin方法具有更高的精度和更高的计算效率。 （C）2018 Elsevier Inc.保留所有权利。

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