Abstract
By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy.
Highlights
Since the construction of the approximation function is independent of the mesh, the meshless method, which has developed rapidly in recent years, can completely abandon the mesh reconstruction to ensure high calculation accuracy [1,2,3]
2.96×10 of the element-free Galerkin (EFG) method in solving singularly perturbed fluid problems, a DS-GIEFG met for singularly perturbed steady CDR problems is proposed in this paper by construc the trial functions based on the improved interpolated moving least squares (IIMLS) method and coupling the dimension splitting method (DSM) and generalized element-free Galerkin (GEFG) meth
The stabilization parameter of the DS-GIEFG method is only related to the nodes and
Summary
Since the construction of the approximation function is independent of the mesh, the meshless method, which has developed rapidly in recent years, can completely abandon the mesh reconstruction to ensure high calculation accuracy [1,2,3]. Since the shape function of the MLS approximation does not satisfy the Kronecker delta property [15], additional numerical techniques are required to impose essential boundary conditions, such as Lagrange multipliers, a penalty method, which may increase the computational burden. Since the singularity of the weight function is not conducive to numerical calculation, Cheng et al proposed an improved interpolated moving least squares (IIMLS) method with nonsingular weights for potential problems [16].
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