Geometric feature-based non-uniform rectangular mesh generation approach

doi:10.11996/JG.j.2095-302X.2025040818

Abstract

Abstract:

The target object for simulating complex electromagnetic environments typically exhibits high geometric complexity, multi-scale geometric features, and a large number of components. To ensure both low computational cost and high geometric resolution, non-uniform rectangular meshes were employed to divide the computational domain for the finite-difference time domain (FDTD) method. In this paper, an automatic approach was proposed for generating non-uniform rectangular meshes based on geometric features. Firstly, a feature extraction algorithm for the discrete facets of CAD models was applied to capture the curvature and thickness features. Secondly, according to the extracted geometric features and user-defined refinement settings, the local size functions reflecting the desired mesh step size were constructed along each coordinate system direction separately. Finally, the locations of mesh nodes on each coordinate axis were calculated according to the local size functions, and then the material properties were assigned to the corresponding mesh cells. Numerical results demonstrated that the proposed approach was remarkably effective in generating non-uniform rectangular meshes for complex geometry models, and has been successfully applied to the time-domain full-wave electromagnetic simulations for complex electrically large size targets.

Key words: mesh generation, non-uniform rectangular mesh, geometric feature, numerical simulation, finite- difference time domain method

CLC Number:

O441
O241.82

LENG Juelin, XU Quan, BAO Xianfeng. Geometric feature-based non-uniform rectangular mesh generation approach[J]. Journal of Graphics, 2025, 46(4): 818-825.

Figures/Tables 17

Fig. 1 Flowchart of non-uniform rectangular mesh generation

Fig. 2 Two dimensional diagram of the three types of geometric features

Fig. 3 Diagram of the sampling method

Fig. 4 Diagram of thickness feature estimation

Fig. 5 Flowchart of local size function creation

Fig. 6 Two dimensional diagram of node position calculation

Fig. 7 Two dimensional diagram of the scan line algorithm

Fig. 8 Geometric models ((a) The ship model; (b) The array antenna model; (c) The unmanned aerial vehicle model)

Table 1 Feature description of the geometric models

模型	几何体/ 个	三角面片/ 个	尺寸跨度/ 量级	特征描述
船	1	2656	2	细杆
阵列天线	13021	449636	3	薄板、小圆柱
无人机	35	254850	4	微带天线结构

Fig. 9 Non-uniform rectangular mesh of the ship model

Fig. 10 Non-uniform rectangular mesh of the array antenna model

Fig. 11 Non-uniform rectangular mesh of the unmanned aerial vehicle model

Table 2 Statistics of test results

模型	网格剖分参数			网格规模/亿	时间/s
模型	最大尺寸	最小尺寸	最大过渡比	网格规模/亿	特征提取	尺寸函数构造	网格线坐标计算	材料编号填充	总计
船	0.20	0.020 0	1.5	0.242	0.095	0.002	0.001	0.430	0.528
阵列天线	0.01	0.000 1	1.5	1.408	65.695	70.185	0.174	14.114	150.168
无人机	0.05	0.001 0	1.5	8.239	3.781	29.239	0.164	9.813	42.997

Fig. 12 Material filling results for the ship model with the same mesh scale ((a) Geometric surface; (b) Non-uniform mesh; (c) Uniform mesh)

Fig. 13 Material filling results for the array antenna model with the same mesh scale ((a) Geometric surface; (b) Non-uniform mesh; (c) Uniform mesh)

Fig. 14 Material filling results for the unmanned aerial vehicle model with the same mesh scale ((a) Geometric surface; (b) Non-uniform mesh; (c) Uniform mesh)

Fig. 15 The integrated coupling simulation results of the unmanned aerial vehicle model with microstrip antenna ((a) Time-domain electric field distribution; (b) Electric field distribution nearby the antenna)

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