Heng Cheng¹, Zebin Xing¹, Miaojuan Peng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 945-964, 2022, DOI:10.32604/cmes.2022.020755

Abstract In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical solutions show that less computational… More >

Zhijuan Meng¹, Yanan Fang¹, Yumin Cheng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 55-79, 2022, DOI:10.32604/cmes.2022.019828

Abstract In this paper, a fast element-free Galerkin (FEFG) method for three-dimensional (3D) elasticity problems is established. The FEFG method is a combination of the improved element-free Galerkin (IEFG) method and the dimension splitting method (DSM). By using the DSM, a 3D problem is converted to a series of 2D ones, and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems. The essential boundary conditions are treated by the penalty method. The splitting direction uses the finite difference method (FDM), which can… More >