基于网格自动剖分技术的复杂腔体电磁特性的有限元法分析
摘要
将矢量有限元方法(EB-FEM)与网格自动剖分技术相结合对复杂腔体中的电磁问题进行分析。利用成熟的3D几何建模软件对所要分析的问题建模并进行网格剖分，并编写通用的接口实现软件与矢量有限元程序之间的数据交换，大大降低了手工剖分带来的过程烦琐以及效率低下等问题，并且将网格剖分和有限元分析分离开来，提高了有限元程序的通用性。利用3D几何建模软件中成熟的算法可以生成高质量的网格，提高了解的精度。通过建模软件结合接口程序可单独提取网格数据，有利于有限元程序的编写，克服了无法从专业电磁软件中提取网格数据的缺点。本文结合自动剖分技术所完成的主要工作包括以下几个方面：
● 应用EB-FEM对复杂形状以及复杂介质填充腔体的谐振频率进行了分析，讨论了运用EB-FEM分析此类问题的优越性，数值结果对实际的谐振腔设计具有参考价值。
● 应用EB-FEM结合完全匹配层(PML)对波导内介质不连续性问题进行了分析。讨论了波导中介质块的数量、介电常数特性与S参数的关系，研究了PML的不同构造对精度的影响。得出了一些对工程设计有参考价值的结论。
● 应用EB-FEM结合边界积分方程对接地腔体的雷达散射面积进行了分析，讨论了腔体内复杂介质填充情况对散射特性的影响，得到了比较精确的结果，讨论了该混合方法在分析此类问题中的优缺点。
In this paper, edge-based finite element method (FEM) is combined with the auto-meshing technique in the analysis of electromagnetic problems related to complex cavities. Geometrical models are established by 3D CAD software and grids are generated automatically. A general interface is designed to exchange data between the CAD software and the FEM program. The complicity and inefficiency in traditional method are greatly decreased. And the interface separates the analysis by FEM from meshing which makes the FEM programs more general in its application to EM problems. Grids of high quality are generated by the arithmetic of the software, and results of computation become more accurate. Grid data is generated independently and the FEM programs are more easily to write. The main work included in the paper is as follows:
Resonant frequencies of cavities with complicated shapes or complex materials filled are analyzed . The advantages of FEM in analyzing such problems are also mentioned , which are useful in the design of resonant cavities.
The problems of waveguide discontinuities are analyzed by FEM combined with PML. The relationship between the S parameters and the amounts of dielectric cubes as well as the permittivity of the dielectric is also discussed. Some useful conclusions are also obtained.
The radar cross section of grounded open cavities is computed by FEM combined with Boundary Integral Equation Method. The cavities filled with complex materials are also analyzed. Accurate results have been obtained. Advantages of this hybrid method in the analysis of such problems are pointed out.
● 应用EB-FEM对复杂形状以及复杂介质填充腔体的谐振频率进行了分析，讨论了运用EB-FEM分析此类问题的优越性，数值结果对实际的谐振腔设计具有参考价值。
● 应用EB-FEM结合完全匹配层(PML)对波导内介质不连续性问题进行了分析。讨论了波导中介质块的数量、介电常数特性与S参数的关系，研究了PML的不同构造对精度的影响。得出了一些对工程设计有参考价值的结论。
● 应用EB-FEM结合边界积分方程对接地腔体的雷达散射面积进行了分析，讨论了腔体内复杂介质填充情况对散射特性的影响，得到了比较精确的结果，讨论了该混合方法在分析此类问题中的优缺点。
In this paper, edge-based finite element method (FEM) is combined with the auto-meshing technique in the analysis of electromagnetic problems related to complex cavities. Geometrical models are established by 3D CAD software and grids are generated automatically. A general interface is designed to exchange data between the CAD software and the FEM program. The complicity and inefficiency in traditional method are greatly decreased. And the interface separates the analysis by FEM from meshing which makes the FEM programs more general in its application to EM problems. Grids of high quality are generated by the arithmetic of the software, and results of computation become more accurate. Grid data is generated independently and the FEM programs are more easily to write. The main work included in the paper is as follows:
Resonant frequencies of cavities with complicated shapes or complex materials filled are analyzed . The advantages of FEM in analyzing such problems are also mentioned , which are useful in the design of resonant cavities.
The problems of waveguide discontinuities are analyzed by FEM combined with PML. The relationship between the S parameters and the amounts of dielectric cubes as well as the permittivity of the dielectric is also discussed. Some useful conclusions are also obtained.
The radar cross section of grounded open cavities is computed by FEM combined with Boundary Integral Equation Method. The cavities filled with complex materials are also analyzed. Accurate results have been obtained. Advantages of this hybrid method in the analysis of such problems are pointed out.
引文
1．(美)金建铭．王建国译．电磁场有限元法 西安：西安电子科技大学出版社出版
2．何小祥 博士论文 基于有限元法的混合技术及其在复杂电大腔体电磁分析中的应用2003．12
3. J.M. Jin and J. L. Volakis. TE scattering by an inhomogeneously filled aperture in a thick conducting plane. IEEE Trans. Antennas Propagat.,1990, vol.AP-38, pp.1280～1286.
4．丁卫平，徐金平．带有腔体或槽缝的电大尺寸目标电磁散射特性分析．电子学报，2002，vol-30(6)，pp．815～818．
5．丁卫平，徐金平．背腔式微带天线电磁散射分析的FEM／PO-PTD方法．电波科学学波，2002，Vol．-17(4)，pp．365～369．
5．盛新庆，徐善驾．有间隙Ⅱ-Ⅵ族半导体材料散射特性的三维边缘元分析．红外与毫米波学报，1996，vol．15(6)，pp．401～406
6．徐欧，何小祥，徐金平．波导不连续性问题的FEM／PML方法分析．微波学报．2003 vol．19(2)，pp．49～52．
7．杨宁，何小祥，丁卫平，徐金平．FE-BI方法分析各向异性介质填充缝隙的散射特性．第十七届南京地区研究生通信年会，2002，pp．745～749．
8．徐欧，何小祥，徐金平．多介质块加载波导散射问题的FEM／PML方法分析．第十七届南京地区研究生通信年会，2002，pp．755～760．
9. JS Wang and N Ida, Eigenvalue analysis in electromagnetic cavities using divergence free finite elements, IEEE Trans. Magnetics, Sept. 1991, vol. MAG-27, pp1985-1999
10．曹世昌．电磁场的数值计算和微波的计算机辅助设计[M]．北京：电子工业出版社。1989
11. Webb, J. P. The finite element method for finding the modes of dielectric-loaded cavities. IEEE Trans., 1985, MTT-33(7), pp.635～639
12. J.P. webb. Efficient generation of divergence-free fields for the finite element analysis of 3D cavity resonances. IEEE Tans. on Magnetics, 1988, vol.24(1).
13. Konrad, A. A direct three-dimensional finite element method for the solution of electromagnetic fields in cavities. IEEE Trans., 1985, MAG-21(6), pp.2276～2279
14．徐善驾、贾冬炎．导波结构三维不连续性问题的高次六面体边缘元分析，电子与信息学报，2001，vol．23(2)，PP．160～167．
15. J.P. Berenger. A perfectly matched layer for the absorption of electromagnetic waves,J. Computational Phys., 1994, vol. 114(2), pp. 185～200.
16. Z.A. Sacks et al. A perfectly matched anisotropic absorber for use as an absorbing boundary condition. IEEE Trans. Antennas Propagat., 1995, vol.43(12), pp. 1460～1463.
17. J.Y. Wu et al. A comparison of anisotropic PML to Berenger's PML and it's application to the finite-element method for EM scattering. IEEE Trans. Antennas Propagat., 1997,vol.45(1), pp.40～50.
18．卞军峰、余春、钟顺时．采用PML吸收边界条件的FDTD法在分析波导不连续性中的应用．上海大学学报，2002，v01．8(1)，pp．7～10．
19．章文勋．电磁场工程中的泛函方法．上海：上海科学技术文献出版社，1985．
20．楼仁海、符果行、肖书君．工程电磁理论．北京：国防工业出版社，1991．
21. Jin J M. Electromagnetic scattering from large deep and arbitrarily-shaped open cavities. [J] Electromagnetics. 1998, vol. 18(1), pp:3～34.
22. Ru-Shan Chen, et. al. Application of the SSOR preconditioned CG algorithm to the vector FEM for 3-D full wave analysis of electromagnetic-field Boundary-value problems. IEEE Trans. On MTT, 2002, Vol-50(4), pp. 1165～1171.
23. Patrizia Savi, et. al. Full wave high order FEM model for lossy anisotropic waveguides.IEEE Trans. On MTT, 2002, Vol-50(2), pp.495～499.
24. Jiao, D., Jian-Ming Jin. Time-domain finite element modeling of dispersive media IEEE Antennas and Propagation Society 2001 IEEE International Sym., vol.3
26. Wang, Tai-Mo; and Ling, Hao: Electromagnetic Scattering From Three-Dimensional Cavities Via a Connection Scheme.IEEE Trans. Antennas & Propag., vol. 39, Oct. 1991,pp. 1505-1513.
27. Pathak, Prabhakar H.; and Burkholder, Robert J.: Modal, Ray, and Beam Techniques for Analyzing the EM Scattering by Open-Ended Waveguide Cavities. IEEE Trans. Antennas & Propag., vol. 37, May 1989, pp. 635-647.
28. Taflove, A.; and Umashankar, K. R.: The Finite-Difference Time-Domain (FD-TD) Method for Electromagnetic Scattering and Interaction Problems. J. Electromagn. Waves & Appl., vol. 1, no. 3, 1987, pp. 243-267.
29. Senior, T. B. A.: Electromagnetic Field Penetration Into a Cylindrical Cavity. IEEE Trans. Electromagn. Compat.,vol. EMC-18, May 1976, pp. 71-73.
30. Mautz, J. R.; and Harrington, R. F.: Electromagnetic Penetration Into a Conducting Circular Cylinder Through a NarrowSlot, TM Case. J. Electromagn. Waves & Appl., vol.2, nos. 3-4, 1988, pp. 269-293
31．周乐柱．边棱元法—一种模拟和分析电磁场的新型计算方法．电子学报，1994，vol．22(12)，PP．1～7．
2．何小祥 博士论文 基于有限元法的混合技术及其在复杂电大腔体电磁分析中的应用2003．12
3. J.M. Jin and J. L. Volakis. TE scattering by an inhomogeneously filled aperture in a thick conducting plane. IEEE Trans. Antennas Propagat.,1990, vol.AP-38, pp.1280～1286.
4．丁卫平，徐金平．带有腔体或槽缝的电大尺寸目标电磁散射特性分析．电子学报，2002，vol-30(6)，pp．815～818．
5．丁卫平，徐金平．背腔式微带天线电磁散射分析的FEM／PO-PTD方法．电波科学学波，2002，Vol．-17(4)，pp．365～369．
5．盛新庆，徐善驾．有间隙Ⅱ-Ⅵ族半导体材料散射特性的三维边缘元分析．红外与毫米波学报，1996，vol．15(6)，pp．401～406
6．徐欧，何小祥，徐金平．波导不连续性问题的FEM／PML方法分析．微波学报．2003 vol．19(2)，pp．49～52．
7．杨宁，何小祥，丁卫平，徐金平．FE-BI方法分析各向异性介质填充缝隙的散射特性．第十七届南京地区研究生通信年会，2002，pp．745～749．
8．徐欧，何小祥，徐金平．多介质块加载波导散射问题的FEM／PML方法分析．第十七届南京地区研究生通信年会，2002，pp．755～760．
9. JS Wang and N Ida, Eigenvalue analysis in electromagnetic cavities using divergence free finite elements, IEEE Trans. Magnetics, Sept. 1991, vol. MAG-27, pp1985-1999
10．曹世昌．电磁场的数值计算和微波的计算机辅助设计[M]．北京：电子工业出版社。1989
11. Webb, J. P. The finite element method for finding the modes of dielectric-loaded cavities. IEEE Trans., 1985, MTT-33(7), pp.635～639
12. J.P. webb. Efficient generation of divergence-free fields for the finite element analysis of 3D cavity resonances. IEEE Tans. on Magnetics, 1988, vol.24(1).
13. Konrad, A. A direct three-dimensional finite element method for the solution of electromagnetic fields in cavities. IEEE Trans., 1985, MAG-21(6), pp.2276～2279
14．徐善驾、贾冬炎．导波结构三维不连续性问题的高次六面体边缘元分析，电子与信息学报，2001，vol．23(2)，PP．160～167．
15. J.P. Berenger. A perfectly matched layer for the absorption of electromagnetic waves,J. Computational Phys., 1994, vol. 114(2), pp. 185～200.
16. Z.A. Sacks et al. A perfectly matched anisotropic absorber for use as an absorbing boundary condition. IEEE Trans. Antennas Propagat., 1995, vol.43(12), pp. 1460～1463.
17. J.Y. Wu et al. A comparison of anisotropic PML to Berenger's PML and it's application to the finite-element method for EM scattering. IEEE Trans. Antennas Propagat., 1997,vol.45(1), pp.40～50.
18．卞军峰、余春、钟顺时．采用PML吸收边界条件的FDTD法在分析波导不连续性中的应用．上海大学学报，2002，v01．8(1)，pp．7～10．
19．章文勋．电磁场工程中的泛函方法．上海：上海科学技术文献出版社，1985．
20．楼仁海、符果行、肖书君．工程电磁理论．北京：国防工业出版社，1991．
21. Jin J M. Electromagnetic scattering from large deep and arbitrarily-shaped open cavities. [J] Electromagnetics. 1998, vol. 18(1), pp:3～34.
22. Ru-Shan Chen, et. al. Application of the SSOR preconditioned CG algorithm to the vector FEM for 3-D full wave analysis of electromagnetic-field Boundary-value problems. IEEE Trans. On MTT, 2002, Vol-50(4), pp. 1165～1171.
23. Patrizia Savi, et. al. Full wave high order FEM model for lossy anisotropic waveguides.IEEE Trans. On MTT, 2002, Vol-50(2), pp.495～499.
24. Jiao, D., Jian-Ming Jin. Time-domain finite element modeling of dispersive media IEEE Antennas and Propagation Society 2001 IEEE International Sym., vol.3
26. Wang, Tai-Mo; and Ling, Hao: Electromagnetic Scattering From Three-Dimensional Cavities Via a Connection Scheme.IEEE Trans. Antennas & Propag., vol. 39, Oct. 1991,pp. 1505-1513.
27. Pathak, Prabhakar H.; and Burkholder, Robert J.: Modal, Ray, and Beam Techniques for Analyzing the EM Scattering by Open-Ended Waveguide Cavities. IEEE Trans. Antennas & Propag., vol. 37, May 1989, pp. 635-647.
28. Taflove, A.; and Umashankar, K. R.: The Finite-Difference Time-Domain (FD-TD) Method for Electromagnetic Scattering and Interaction Problems. J. Electromagn. Waves & Appl., vol. 1, no. 3, 1987, pp. 243-267.
29. Senior, T. B. A.: Electromagnetic Field Penetration Into a Cylindrical Cavity. IEEE Trans. Electromagn. Compat.,vol. EMC-18, May 1976, pp. 71-73.
30. Mautz, J. R.; and Harrington, R. F.: Electromagnetic Penetration Into a Conducting Circular Cylinder Through a NarrowSlot, TM Case. J. Electromagn. Waves & Appl., vol.2, nos. 3-4, 1988, pp. 269-293
31．周乐柱．边棱元法—一种模拟和分析电磁场的新型计算方法．电子学报，1994，vol．22(12)，PP．1～7．