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Gmsh algorithm numbering5/4/2023 Moreover, the AVMEFG methods with the two residual-based a posteriori error estimators are generally equivalent except in the case that the solution has an exponential boundary layer, where the energy norm error estimator can achieve significantly better results than the other one.Īdaptive meshing includes local refinement as well as coarsening of meshes. Numerical examples illustrate that the proposed method is effective and efficient in solving the convection-dominated problem involving various layers. Among them, the first example makes a comparison between the proposed method and the adaptive element free Galerkin method, while the other remaining examples compare two different residual-based a posteriori error estimators for the proposed method. Several stationary convection–diffusion–reaction problems are solved to verify the effectiveness of the proposed method. ![]() With respect to the adaptive technique adopted, two residual-based a posteriori error estimators in the H1-semi norm and energy norm are respectively used to locate and remark the high-gradient numerical solution regions. To overcome this shortcoming, we consider incorporating an adaptive algorithm based on the residual error estimations into the VMEFG, which formed the adaptive VMEFG (AVMEFG) method. Then, the proposed method was applied to a 37 kw motor for electromagnetic analysis, and the results obtained proved the accuracy of the algorithm finally, the effectiveness of the mesh movement algorithm in three-dimensional space was tested by moving the sphere inside the cylinder.Īs we know, the variational multiscale element free Galerkin (VMEFG) method may still suffer from non-physical oscillations near the boundary or interior layers when solving the convection–diffusion–reaction problems with strong convection-dominated. The proposed method has the advantages of keeping the original mesh structure and minimum mesh deformation as well as speed up the convergence, save time in the finite element meshing, and ensure the quality of the generated mesh. ![]() In the proposed method, a mesh size function that considers curvature, feature size, and distance gradient restrictions is constructed, which can obtain high quality meshes and avoid excessive iteration when the finite element mesh domain is deformed, only the mesh nodes close to the moving boundary are allowed to move, and the theory of force-balance is used combined with the second-order boundary projection algorithm to perform iterative optimization of the mesh node positions. A moving meshing algorithm with mesh adaptive size function was proposed in this paper with regard to the modeling speed and solution accuracy of electromagnetic equipment in the optimization design process.
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