基于几何特征的非均匀矩形网格生成方法

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

图学学报 ›› 2025, Vol. 46 ›› Issue (4): 818-825.DOI: 10.11996/JG.j.2095-302X.2025040818

• 计算机图形学与虚拟现实 • 上一篇下一篇

基于几何特征的非均匀矩形网格生成方法

冷珏琳¹^,²(), 徐权¹^,², 鲍献丰¹^,²

1.中物院高性能数值模拟软件中心，北京 100088
2.北京应用物理与计算数学研究所，北京 100088

收稿日期:2024-08-13 修回日期:2024-12-26 出版日期:2025-08-30 发布日期:2025-08-11
第一作者:冷珏琳(1988-)，女，副研究员，博士。主要研究方向为计算几何、CAD模型处理和网格生成等。E-mail：leng_juelin@163.com
基金资助:
国家自然科学基金联合基金(U23B2067);国家自然科学基金(12371364);国家自然科学基金(62231003)

Geometric feature-based non-uniform rectangular mesh generation approach

LENG Juelin¹^,²(), XU Quan¹^,², BAO Xianfeng¹^,²

1. China CAEP Software Center for High Performance Numerical Simulation, Beijing 100088, China
2. Institute of Applied Physics and Computational Mathematic, Beijing 100088, China

Received:2024-08-13 Revised:2024-12-26 Published:2025-08-30 Online:2025-08-11
First author：LENG Juelin (1988-), female, associate researcher, Ph.D. Her main research interests cover computational geometry, CAD model processing, and mesh generation. E-mail：leng_juelin@163.com
Supported by:
Joint Funds of the National Natural Science Foundation of China(U23B2067);National Natural Science Foundation of China(12371364);National Natural Science Foundation of China(62231003)

摘要/Abstract

摘要：

复杂电磁环境模拟的目标对象通常具有几何结构复杂、尺寸跨度大、部件数量多的特点。面向时域有限差分方法，需要采用非均匀的矩形网格来剖分计算区域，在保证几何高分辨率的同时，尽量减少内存和计算开销。为此，提出了一种基于几何特征的非均匀矩形网格自动生成方法。首先，采用基于离散面片的特征提取算法获取几何模型的曲率特征和厚度特征；然后，针对提取的几何特征以及用户设置的局部加密参数，在3个坐标方向上分别构造反映网格步长疏密分布的局部尺寸函数；最后，根据尺寸函数计算各坐标方向上的网格线坐标，并填充网格单元的材料属性。测试结果表明，该方法能够自动剖分适应精细几何结构的非均匀矩形网格，并成功应用于复杂电大尺寸目标的时域全波电磁模拟。

关键词: 网格生成, 非均匀矩形网格, 几何特征, 数值模拟, 时域有限差分方法

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

中图分类号:

O441
O241.82

冷珏琳, 徐权, 鲍献丰. 基于几何特征的非均匀矩形网格生成方法[J]. 图学学报, 2025, 46(4): 818-825.

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

图/表 17

图1 非均匀矩形网格生成流程

Fig. 1 Flowchart of non-uniform rectangular mesh generation

图2 3类几何特征的二维示意图

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

图3 采样方法示意图

Fig. 3 Diagram of the sampling method

图4 厚度特征计算示意图

Fig. 4 Diagram of thickness feature estimation

图5 局部尺寸函数构造流程图

Fig. 5 Flowchart of local size function creation

图6 二维情况下的网格点坐标计算示意图

Fig. 6 Two dimensional diagram of node position calculation

图7 扫描线算法二维示意图

Fig. 7 Two dimensional diagram of the scan line algorithm

图8 几何模型((a) 船模型；(b) 阵列天线模型；(c) 无人机模型)

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

表1 几何模型特征描述

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

图9 船模型的非均匀矩形网格生成结果

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

图10 阵列天线模型的非均匀矩形网格生成结果

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

图11 无人机模型的非均匀矩形网格生成结果

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

表2 测试结果统计

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

图12 同等网格规模下船模型的材料属性填充结果((a) 几何表面；(b) 非均匀网格；(c) 均匀网格)

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

图13 同等网格规模下阵列天线模型的材料属性填充结果((a) 几何表面；(b) 非均匀网格；(c) 均匀网格)

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)

图14 同等网格规模下无人机模型的材料属性填充结果((a) 几何表面；(b) 非均匀网格；(c) 均匀网格)

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)

图15 强电磁脉冲环境下的无人机-天线一体化耦合计算结果((a) 时域电场分布；(b) 天线附近的电场分布)

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)

参考文献 16

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基于几何特征的非均匀矩形网格生成方法

Geometric feature-based non-uniform rectangular mesh generation approach

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