Automatic Geometry Adaptive Quadrilateral Mesh Generation Using Medial Axis Transform

2001 ◽  
Author(s):  
W. R. Quadros ◽  
K. Ramaswami ◽  
F. B. Prinz ◽  
B. Gurumoorthy
Keyword(s):  
Mesh Generation ◽  
Medial Axis ◽  
Mesh Size ◽  
Geometric Feature ◽  
Medial Axis Transform ◽  
Feature Size ◽  
Quadrilateral Mesh ◽  
Advancing Front ◽  
Radius Function

Abstract The medial axis transform (MAT) has been used in meshing algorithms for decomposition (Tam 1991; Price 1995; Price 1997) and for decomposition and termination (Quadros 2000: Quadros Thesis 2000). This paper describes an algorithm that uses the MAT for quad meshing that is adapted to the variation of geometric feature size in the domain. The algorithm is a modification of Lay Tracks, an automatic quad meshing algorithm that uses the MAT for both subdividing the domain and for terminating the advancing front of the mesh. The modification involves the adaptive placing of nodes inside the subdivided regions and makes use of the radius function available in the MAT to identify feature size and adapt the node spacing and mesh size to it. The algorithm has been implemented and tested on some typical geometries. Results on the quality of the mesh obtained are presented.

Robust and Quality Boundary Constrained Tetrahedral Mesh Generation

2013 ◽  
Vol 14 (5) ◽  
pp. 1304-1321 ◽  
Author(s):  
Songhe Song ◽  
Min Wan ◽  
Shengxi Wang ◽  
Desheng Wang ◽  
Zhengping Zou
Keyword(s):  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Tetrahedral Mesh ◽  
Mesh Optimization ◽  
Surface Mesh ◽  
Triangulated Surface ◽  
Advancing Front ◽  
Novel Method ◽  
Tetrahedral Mesh Generation

AbstractA novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique (AFT) and conforming Delaunay triangulation. Given a triangulated surface mesh, AFT is firstly applied to mesh several layers of elements adjacent to the boundary. The rest of the domain is then meshed by the conforming Delaunay triangulation. The non-conformal interface between two parts of meshes are adjusted. Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality. Robustness and quality of the proposed method is shown. Convergence proof of each stage as well as the whole algorithm is provided. Various numerical examples are included as well as the quality of the meshes.

An automatic approach to constrained quadrilateral mesh generation

2019 ◽  
Vol 37 (3) ◽  
pp. 929-951 ◽  
Author(s):  
Xinwu Ma ◽  
Lu Sun
Keyword(s):  
Laplace Equation ◽  
Mesh Generation ◽  
Design Methodology ◽  
User Interaction ◽  
Mesh Size ◽  
Quadrilateral Mesh ◽  
Content Type ◽  
Internal Feature ◽  
Required Quality ◽  
Feature Constraints

Purpose Arbitrary constraints might be included into the problem domain in many engineering applications, which represent specific features such as multi-domain interfaces, cracks with small yield stresses, stiffeners attached on the plate for reinforcement and so on. To imprint these constraints into the final mesh, additional techniques need to be developed to treat these constraints properly. Design/methodology/approach This paper proposes an automatic approach to generate quadrilateral meshes for the geometric models with complex feature constraints. Firstly, the region is decomposed into sub-regions by the constraints, and then the quadrilateral mesh is generated in each sub-region that satisfies the constraints. A method that deals with constraint lines and points is presented. A distribution function is proposed to represent the distribution of mesh size over the region by using the Laplace equation. The density lines and points can be specified inside the region and reasonable mesh size distribution can be obtained by solving the Laplace equation. Findings An automatic method to define sub-regions is presented, and the user interaction can be avoided. An algorithm for constructing loops from constraint lines is proposed, which can deal with the randomly distributed constraint lines in a general way. A method is developed to deal with constraint points and quality elements can be generated around constraint points. A function defining the distribution of mesh size is put forward. The examples of constrained quadrilateral mesh generation in actual engineering analysis are presented to show the performance of the approach. Originality/value An automatic approach to constrained quadrilateral mesh generation is presented in this paper. It can generate required quality meshes for special applications with complex internal feature constraints.

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