多层/多孔材料在特定几何剖分下电磁时域有限差分法的散射分析

张玉贤; 杨子江; 黄志祥; 冯晓丽; 冯乃星; 杨利霞

doi:10.11999/JEIT250348

多层/多孔材料在特定几何剖分下电磁时域有限差分法的散射分析

doi: 10.11999/JEIT250348 cstr: 32379.14.JEIT250348

张玉贤^{1, 2, 3},
杨子江¹,
黄志祥^{1, 2, 4},
冯晓丽⁴,
冯乃星^{1, 2},
杨利霞^{1, 3}

1.
安徽大学电子信息工程学院合肥 230601
2.
安徽大学信息材料与智能感知安徽省实验室合肥 230601
3.
安徽大学光电信息获取与防护技术全国重点实验室合肥 203601
4.
安徽大学集成电路先进材料与技术产教研融合研究院合肥 203601

基金项目: 通信作者：黄志祥 07027@ahu.edu.cn：国家自然科学基金(62101333, 62531001)；2024年安徽省高校理工科教师赴企业挂职实践计划项目(2024jsqygz02)；2024年安徽省研究生教育质量工程任务(2024cxcyjs004)

详细信息

作者简介:
张玉贤：男，副教授，研究方向为计算电磁学、电磁逆时偏移成像技术

杨子江：男，博士研究生，研究方向为计算电磁学、复杂几何建模设计

黄志祥：男，教授，研究方向为计算电磁学、多物理场理论研究

冯晓丽：女，助理工程师，研究方向为集成电路工艺设计

冯乃星：男，副教授，研究方向为计算电磁学、机器学习

杨利霞：男，教授，研究方向为时域有限差分法、等离子体物理

中图分类号: TN95; O441.4
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- 文章访问数: 11
- HTML全文浏览量: 3
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- 被引次数: 0
出版历程
- 收稿日期: 2025-05-06
- 修回日期: 2025-10-10
- 网络出版日期: 2025-10-20

Electromagnetic Finite-Difference Time-Domain Scattering Analysis of Multilayered/Porous Materials in Specific Geometric Meshing

ZHANG Yuxian^{1, 2, 3},
YANG Zijiang¹,
HUANG Zhixiang^{1, 2, 4},
FENG Xiaoli⁴,
FENG Naixing^{1, 2},
YANG Lixia^{1, 3}

1.
School of Electronic and Information Engineering, Anhui University, Hefei 230601, China
2.
Materials and Intelligent Sensing Laboratory of Anhui Province, Hefei 230601, China
3.
National Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology, Hefei 230601, China
4.
Industry-Education-Research Institute of Advanced Materials and Technology for Integrated Circuits, Hefei 230601, China

Funds: National Natural Science Foundation of China (62101333, 62531001), 2024 Program for Teachers of Science and Engineering in Colleges and Universities of Anhui Province to Take Temporary Positions in Enterprises (2024jsqygz02), 2024 Task of Postgraduate Education Quality Project of Anhui Province (2024cxcyjs004)

摘要

摘要: 时域有限差分法(FDTD)作为计算介质电磁特性的有效方法，往往受到模型结构及其网格剖分的预处理限制。为了探究多层/多孔材料的电磁散射特性问题，提高电磁仿真的计算效率，该文提出一种基于FDTD的电磁分析加速方案。通过计算几何算法来快速完成复杂材料的Yee网格划分，由三维体素数组定义材料构建分布矩阵与电磁分量的统一排布，针对体素数据的特点实现了非解析几何介质的雷达散射截面的高效计算。现今大多数体网格剖分需要解析公式来描述几何体，该文开创性地将射线求交法与有向距离相结合，并通过切平面与交点计算减少网格生成过程中的无效遍历、降低几何运算复杂度，加速实现多孔非解析几何体的电磁参数网格化定义。该文设计了3种关于多层/多孔材料的时域电磁分析场景，计算了这些场景在不同条件下的雷达散射截面。与主流电磁仿真软件任意复杂电磁场计算(FEldberechnungbei Korpern mit beliebiger Oberflache, FEKO)、计算机仿真技术(Computer Simulation Technology, CST)和高频结构仿真软件(High Frequency Structure Simulator, HFSS)的计算相比，该方法的计算数据呈现出高度的吻合性，表现出了优越的效率。电磁分析加速方案拓展了使用FDTD进行电磁仿真的介质结构及材料类型，在保证计算精度的前提下显著节省了计算时间与内存，为体网格剖分加速和内部结构处理提供了新的研究思绪。
- 电磁散射问题 /
- 时域有限差分法 /
- 网格剖分 /
- 多层/多孔材料
Abstract: The Finite-Difference Time-Domain (FDTD) method is a widely used tool for analyzing the electromagnetic properties of dielectric media, but its application is often constrained by model complexity and mesh discretization. To enhance the efficiency of electromagnetic scattering simulations in multilayered/porous materials, we proposes an accelerated FDTD scheme in this paper. Computational geometry algorithms can be employed with the proposed method to rapidly generate Yee’s grids, utilizing a three-dimensional voxel array to define material distributions and field components. By exploiting the voxel characteristics, parallel algorithms are employed to efficiently compute Radar Cross Sections (RCS) for non-analytical geometries. In contrast to conventional volumetric mesh generation, which relies on analytic formulas, this work integrates ray-intersection techniques with Signed Distance Functions (SDFs). Calculations of tangent planes and intersection points minimize invalid traversals and reduce computational complexity, thus expediting grid-based electromagnetic parameter assignment for porous and irregular structures. The approach is applied to the RCS calculations of multilayered/porous models, demonstrating excellent consistency with results from popular commercial solvers (FEKO, CST, HFSS) while offering substantially higher efficiency. Numerical experiments confirm significant reductions in computation time and computer memory without compromising accuracy. Overall, the proposed acceleration scheme enhances the FDTD method’s ability to handle complex dielectric structures, providing an effective balance between computational speed and accuracy, and offering innovative solutions for rapid mesh generation and processing of complex internal geometries. Objective The FDTD method, a reliable approach for computing the electromagnetic properties of dielectric media, faces constraints in computational efficiency and accuracy due to model structure and mesh discretization. A major challenge in the field is achieving efficient electromagnetic scattering analysis with minimal computational resources while maintaining sufficient wavelength sampling resolution. To address this difficulty, we propose an FDTD-based electromagnetic analysis acceleration scheme that enhances simulation efficiency by significantly improving mesh generation and optimizing grid partitioning for complex multilayered/porous models. Methods In this study, those Yee’s grids for complex materials are efficiently generated using computational geometry algorithms and a 3D voxel array to define material distribution and field components. A parallel algorithm leverages voxel data to accelerate RCS calculations for non-analytical geometries. Unlike conventional volumetric meshing methods that rely on analytic formulas, this approach integrates ray-intersection techniques with SDFs. Calculations of tangent planes and intersection points further reduce invalid traversals and geometric complexity, facilitating faster grid-based assignment of electromagnetic parameters. Numerical experiments validate that the method effectively supports porous and multilayered non-analytical structures, demonstrating both high efficiency and accuracy. Results and Discussions The accelerated volumetric meshing algorithm is validated using a Boeing 737 model, showing more than a 67.5% reduction in computation time across different resolutions. Efficiency decreases at very fine meshes because of heavier computational loads and suboptimal valid-grid ratios. The method is further evaluated on three multilayered/porous structures, achieving 85.55% faster computation and 9.8% lower memory usage compared with conventional FDTD. In comparison with commercial solvers (FEKO, CST, HFSS), equivalent accuracy is maintained while runtimes are reduced by 87.58% and memory consumption by 81.6%. In all tested cases, errors remain below 6% relative to high-resolution FDTD, confirming that the proposed acceleration scheme provides both high efficiency and reliable accuracy. Conclusions In this study, we optimize volumetric mesh generation in FDTD through computational geometry algorithms. By combining ray-intersection techniques with reliable SDFs, the proposed approach efficiently manages internal cavities, while tangent-plane calculations minimize traversal operations and complexity, thereby accelerating scattering analysis. The scheme extends the applicability of FDTD to a broader range of dielectric structures and materials, delivering substantial savings in computation time and memory without compromising accuracy. Designed to support universal geometric model files, the framework shows strong potential for stealth optimization of multi-material structures and the development of electromagnetic scattering systems. It represents an important step toward integrating computational geometry with computational electromagnetics.
- Electromagnetic scattering /
- Finite-Difference Time-Domain (FDTD) method /
- Mesh generation /
- Multilayered/porous materials

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图 1 波音737喷气式客机模型及不同精度下立方体网格结构

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图 2 射线求交法交点奇偶性判别法的缺陷

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图 3 网格生成算法整体流程图

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图 4 3层介质球在斜入射高斯光源下的模型图和立方体网络结构图

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图 5 3层介质球在xOy,xOz和 yOz 平面下的1 GHz双站RCS极坐标计算结果

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图 6 随机位置空腔的矩形盒与入射光源示意图

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图 7 多孔介质矩形盒在xOy, xOz, yOz 平面下的1 GHz双站RCS极坐标计算结果

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图 8 双层多孔固液介质球的网格结构及入射光源示意图与高密度下网格结构图

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图 9 双层多孔介质球在xOy, xOz, yOz 平面下的1 GHz双站RCS极坐标计算结果

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表 1 传统及加速算法在不同精度下的网格数与计算耗时对比

方法	模型标号	网格总数	有效网格数	标准计算耗时 (s)	内存峰值 (GB)	CPU占用率 (%)	网格边长 (m)
遍历剖分	-	764 209	7 718	11.74	0.73	11	0.5
	(b)	3 018 600	298 871	48.28	1.05	13	0.25
	(c)	9 773 114	99 170	269.67	1.40	21	0.15
加速算法	-	764 209	7 718	2.24	1.27	12	0.5
	(b)	3 018 600	298 871	12.08	1.75	18	0.25
	(c)	9 773 114	99 170	87.83	2.26	24	0.15

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表 2 有符号距离与射线求交法结合判别几何位置

交点个数	距离的正负	网格点位置
奇数	负数	模型内部
奇数	正数	孔洞外表面附近
偶数	正数	模型外部
偶数	负数	孔洞内部

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表 3 3层球体下4种方法的范数误差与计算资源对比

方法	每波长采样(PPW)	网格数	内存	CPU时间(s)	L₂范数误差(×10^–2)
FDTD	8.94	250 047	244.10 MB	16.27	4.35
FEKO	12.00	4 252	1.31 GB	398.93	3.15
CST	5.00	4 232	1.27 GB	131.02	5.37
HFSS	4.78	28 347	341.45 MB	27.09	4.79

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表 4 多孔各向同性矩形盒的范数误差与计算资源对比

方法	每波长采样(PPW)	网格数	内存(MB)	CPU时间(s)	L₂范数误差
FDTD	26.83	575 113	410.7	16.27	3.21×10^–3
FEKO	12.00	3 212	567.4	230.18	2.51×10^–2
CST	5.00	2 814	783.5	22.62	3.78×10^–2
HFSS	3.44	10 210	482.7	27.32	2.91×10^–2

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表 5 双层多孔介质球的范数误差与计算资源对比

方法	每波长采样(PPW)	网格数	内存	CPU时间(s)	L₂范数误差(×10^–2)
FDTD	18.67	1 984 500	574.15 MB	26.34	5.65
FEKO	12.00	3 358	606.11 MB	207.97	4.22
CST	5.00	2 882	779.32 MB	28.56	5.47
HFSS	16.74	37 900	2.26 GB	57.42	4.12

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