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用精细积分法对含各向异性介质的波导不连续性问题进行了数值模拟与分析. 从矢量波动方程相对应的单变量变分形式出发, 推导出了含有各向异性介质波导横截面离散系数矩阵的表达式, 引入对偶变量, 在Hamilton体系下, 利用精细积分法求出出口刚度矩阵, 进行有限元拼装, 求解了含各向异性介质的波导不连续性问题. 算例表明了该方法的准确性和高效性. 利用本文方法还讨论了介电系数和导磁系数张量的各个分量对波导传输特性的影响.
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关键词:
- 波导不连续性 /
- 各向异性介质 /
- Hamilton体系 /
- 精细积分法
Waveguide discontinuities with anisotropic dielectric are simulated and analyzed by the precise integration method. The discrete coefficient matrices for the cross-section of the waveguide, which contains anisotropic dielectric, are deduced from the variational principle based on single variable corresponding to the vector wave equation. Introducing the dual-variables, the stiff matrices are calculated by using precise integration method in a Hamiltonion system. Then the problem is solved by assembling the finite elements. Numerical results show accuracy and good efficiency of the method. The influence of the components of permittivity and permeability on the waveguide transmission characteristic is also discussed.-
Keywords:
- waveguide discontinuity /
- anisotropic dielectric /
- Hamilton system /
- precise integration method
[1] Rahman B M A, Davies J B 1988 IEEE J. Lightwave Tecnol. 6 52
[2] Yang R, Xie Y J, Wang Y Y, Fu H Z 2008 Acta Phys. Sin. 57 5513 (in Chinese) [杨锐, 谢拥军, 王元源, 傅焕展 2008 57 5513]
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[6] Bian J F, Yu C, Zhong S S 2002 J. Shanghai Univ. Natural Science Edition 8 7 (in Chinese) [卞军峰, 余春, 钟顺时 2002 上海大学学报 (自然科学版) 8 7]
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[10] Zhong W X 2002 Dual System in Applied Mechanics (Beijing: Science Press) p24 (in Chinese) [钟万勰 2002 应用力学对偶体系 (北京: 科学出版社) 第24页]
[11] Zhong W X, Zhu J P 1996 J. Num. Meth. Comput. Appl. 1 26 (in Chinese) [钟万勰, 朱建平 1996 数值计算与计算机应用 1 26]
[12] Zhong W X 2001 J. Dalian Univ. Technol. 41 379 (in Chinese) [钟万勰 2001 大连理工大学学报 41 379]
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[1] Rahman B M A, Davies J B 1988 IEEE J. Lightwave Tecnol. 6 52
[2] Yang R, Xie Y J, Wang Y Y, Fu H Z 2008 Acta Phys. Sin. 57 5513 (in Chinese) [杨锐, 谢拥军, 王元源, 傅焕展 2008 57 5513]
[3] Gong J Q, Liang C H 2011 Acta Phys. Sin. 60 059204 (in Chinese) [龚建强, 梁昌洪 2011 60 059204]
[4] Cheng J F, Xu S J 2001 Acta Electron. Sin. 29 708 (in Chinese) [程军峰, 徐善驾 2001 电子学报 29 708]
[5] Jin J M 2002 The Finite Element Method in Electromagnetics (2nd Edn.) (New York: John Wiley & Sons) p126
[6] Bian J F, Yu C, Zhong S S 2002 J. Shanghai Univ. Natural Science Edition 8 7 (in Chinese) [卞军峰, 余春, 钟顺时 2002 上海大学学报 (自然科学版) 8 7]
[7] Zhou P, Xu J P 2004 J. Microw. 20 43 (in Chinese) [周平, 徐金平 2004 微波学报 20 43]
[8] Zhao W, Zhao Y J, Lu H M 2008 J. Xidian Univ. Nat. Sci. Ed. 35 894 (in Chinese) [赵伟, 赵永久, 路宏敏 2008 西安电子科技大学学报 (自然科学版) 35 894]
[9] Chen J F, Zhu B, Zhong W X 2009 Acta Phys. Sin. 58 1091 (in Chinese) [陈杰夫, 朱宝, 钟万勰 2009 58 1091]
[10] Zhong W X 2002 Dual System in Applied Mechanics (Beijing: Science Press) p24 (in Chinese) [钟万勰 2002 应用力学对偶体系 (北京: 科学出版社) 第24页]
[11] Zhong W X, Zhu J P 1996 J. Num. Meth. Comput. Appl. 1 26 (in Chinese) [钟万勰, 朱建平 1996 数值计算与计算机应用 1 26]
[12] Zhong W X 2001 J. Dalian Univ. Technol. 41 379 (in Chinese) [钟万勰 2001 大连理工大学学报 41 379]
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