Research On Generation Method Of Multi-constrained Quadrilateral Mesh Based On Frame Field

Mesh generation is one of the preprocessing steps in numerical simulation.For complex models,mesh generation is a main performance bottleneck in the numerical simulation process.Compared to triangular meshes,quadrilateral meshes can better fit the boundary curvature of the model and perform well in finite element simulations and surface modeling applications,making them highly regarded.However,generating high-quality quadrilateral meshes automatically for complex models remains challenging.Currently,two main quadrilateral mesh generation methods exist for complex models:(1)engineers manually decompose the model into regular quadrilateral partitions and then generate structured meshes within each partition.However,this method requires engineers to have strong engineering experience,is very time-consuming,and there is a possibility of errors;(2)various fully automatic methods are used to generate unstructured meshes,but these methods generate meshes of poor quality and contain many irregular singular points.Given the above problem background,this dissertation proposes a plane quadrilateral mesh generation method under multiple feature constraints.To achieve the generality of the method,it is extended to three-dimensional surfaces,and a surface quadrilateral mesh generation method based on the Riemann frame field is proposed.This method can automatically generate high-quality quadrilateral meshes while maintaining multiple geometric and size constraints specified by the user.The work of this dissertation is summarized as follows:1.A plane quadrilateral mesh generation method under multiple feature constraints is proposed.First,this method uses the heat diffusion projection iteration method to solve the Ginzburg-Landau equation to obtain a frame field that meets the feature constraints.Then,the problem of constructing partitions within the frame field is transformed into a network flow problem,and the minimum cost maximum flow algorithm is used to solve it,decomposing the model into multiple sub-partitions.Then,an integer linear programming model is constructed for all partition lines,determining each partition’s discrete mesh edge numbers,and using the “general pattern” strategy to quadrilateralize each partition.2.A surface quadrilateral mesh generation method is proposed based on the Riemann frame field.First,a Riemann frame field model is established on the surface to obtain a frame field that meets the feature constraints defined on the surface model.Then,size constraints and “simple pattern” strategy constraints are introduced in the partition construction to quadrilateralize non-quadrilateral partitions as much as possible.When determining the discrete mesh edge numbers of partition lines,non-quadrilateral partition regularity objectives and singular point alignment objectives are introduced,and the “general pattern” and “simple pattern” strategies are combined to quadrilateralize each partition.