波束波导电磁传输和辐射理论建模与高效算法研究
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摘要
对波束波导(BWG)传输系统的精确建模与高效数值分析是计算电磁学领域的难点。它通常具有电大尺寸、复杂异形传输结构、金属-介质混合结构。这些特征导致数值求解过程中计算量极大、迭代收敛缓慢。本文采用积分方程(IE)与模式匹配(MM)相结合的方法简化模型，并利用预条件技术加速迭代收敛。在处理电大尺寸问题时我们采用多层快速多极子算法(MLFMA)。该算法通过加法定理对自由空间格林函数进行分解，使用聚合、转移、配置的方式，将积分方程方法求解过程中的计算和存储复杂度降至O (N log N)。在一体化建模和计算的框架下，对电大尺寸复杂结构的波束波导的传输问题进行快速精确求解。此外，对在有限口径的喇叭馈源照射下任意数量、形状、位置的反射面的散射也能高效求解。在实际应用中，可利用上述方法高效求解带有介质罩的天线、频率选择表面及大型偏馈反射面天线的辐射和散射特性。
本文首先介绍了复杂结构辐射、散射与传输特性分析领域中的传统数值方法，包括解析方法，高频方法，微分方程方法，积分方程方法，混合方法。然后深入论述基函数以及矩量法。最后，将传统的积分方程方法与模式匹配方法相结合，建立了波导馈电的腔体问题的等效模型。
通过研究波导的等效模型，获得了对波导馈电的电大尺寸复杂结构激励、传输与辐射的高效数值求解策略。本文研究了波导馈电的电大尺寸结构（包括金属、金属-介质混合结构的波束波导、多波导端口辐射器）的传输和辐射问题的精确电磁建模与高效计算的数值方法，并选用多层快速多极子算法进行快速求解。
使用上述方法仅需对待求结构中的金属表面和介质体区域进行离散。而通常的波束波导恰好具有电大尺寸的金属表面和大量的无需剖分的空域，这使得采用积分方程方法与采用微分方程方法相比，极大地降低了未知量，提高了求解效率。使用波导模式匹配方法，考虑各导波模式的反射影响，可得到激励口面处的场匹配状况，并最终获得精确的场解。
在此基础上，对上述方法进行扩展后可对多波导端口馈电的天线阵列给出精确的场解。当这种天线阵列的阵元数目增多，整体电尺寸变大，且阵列中可能存在不同结构的阵元，其间又存在复杂的电磁耦合。这导致数值仿真需要耗费大量的计算资源，甚至无法计算。本论文提供的等效模型和高效算法则可求解多个馈源、各个馈源可具任意形态和结构、各个辐射结构可具任意的馈电模式、各馈源间可有任意的相对位置的传输与辐射问题。
为进一步提高对电大尺寸波束波导传输特性的求解效率，采用了相位提取(PE)基函数来描述电流。这样做的根据是波束波导内部金属表面上的感应电流在入射波方向上呈周期性变化。与传统的基函数比较而言，PE基函数可以被定义在更大的贴片上。使用PE基函数直接地减少了待求未知量，极大地增强了求解电大尺寸波束波导问题的能力。
在迭代求解过程中，成功的将预条件方法应用到本文方法中，得到了显著的效果。此外，本文研究的算法在结合OpenMP并行计算技术之后，计算能力得到了大幅的提升。作者依据本文方法开发完成了相应的数值仿真程序，并得到了数值算例的验证。
The accurate modeling and efficient solving of the beam waveguide(BWG)transmission system is always a challenge in the computational electromagnetics. Thebeam waveguide always has large size compared with the wavelength, complexstructure, and composite metallic-material structure. It cause the huge computation loadand the slow iteration process. In this thesis, the integral equation(IE) method and themode matching(MM) method are combined together to simplify the model, and thepreconditioning technique is used to accelerate the convergence speed. To deal with thestructure of electrically large size, the multilevel fast multipole algorithm(MLFMA) isused. Decomposing the free space Green’s function by the style of aggregation,transformation and disaggregation, MLFMA successfully reduces the computationcomplexity to O (N log N). The transmission problems of beam waveguide withelectronically large size and complex structure can be solved efficiently by using thisintegrated modelling and simulation environment. The characteristics of reflectors withany number, arbitrary shape, and arbitrary position while illuminated by the horn feedcan be solved efficiently. In practical application, the method mentioned above can beused to obtain the radiation and scattering characteristics of the radomes, the frequencyselective surfaces, and the large side-fed reflector antennas efficiently.
First, the traditional numerical methods of solving the excitation, transmission andradiation problems of the complex structure are introduced. Including the analyticalmethod, the high-frequency method, the differential equation method, the integralequation method and the hybrid method. The basis functions and the method of momentare deeply studyed. Finally, the integral equation method is combined with the modematching method and the equivalent model of the waveguide-fed cavities.
By studying the equivalent model of the waveguide, we got the efficient numericalmethod of solving the excitation, transmission and radiation problems of theelectrically-large and complex beam waveguide structures. We have discussed theaccurate modeling and effective numerical solving of the transmission and radiation ofthe waveguide-fed electrically-large structure problems(including the conductor or thecomposite metallic-material beam waveguide and the arbitrary multi-port radiation structures). Then the MLFMA is used to improve the efficiency of the solving process.
Using the integral equation method, we only need to discrete the surface of the ideaconductor and the volume of the dielectric area. The characteristic of the beamwaveguide always contains large space without any PEC or volumn structure. Then thenumber of unknowns is much less and the solving efficiency is much higher comparedby using the differential equation methods. Using the mode matching method, andconsidering the reflecting guide wave modes, we can get the matching situation on theexciting erea and the accurate results.
The method of dealing with the single waveguide-fed problem is expanded tosimulate the multi-port waveguide-fed antenna array problems. The increasing numberof antenna elements brings the large electrical size. And there are always the elementswith different structure and feeding mode and the complex electromagnetic coupling.The requirement of computing resource is great, which even cannot be supplied. Themodel and efficient algorithm raised in this thesis can deal with the multi-portwaveguide-fed transmission and radiation problems with feeds of arbitrary amount,structure, excitation mode and relative position.
In order to further improve the efficient of solving the transmission problems of thebeam waveguide with electrically large size structure, we used the phase-extracted(PE)basis functions to describe the surface electric current. The reason is that the phase ofthe electric induced current on the PEC surface of the beam waveguide changeperiodically along the direction of the incident wave. Comparing with the traditionalbasis functions, the PE basis function can be defined on the larger patches. Using thisbasis function, the unknowns is directly reduced and the ability of solving the beamwaveguide with electronically large size is greatly improved.
In the solving process, the preconditioning technique is used, and the better effectis got. Moreover, the OpenMP parallel technique is adopted and the solving efficiency isgreatly improved. The author has been developed the program codes based on themethods mentioned in this dissertation, which is validated by the numerical experiment.
本文首先介绍了复杂结构辐射、散射与传输特性分析领域中的传统数值方法，包括解析方法，高频方法，微分方程方法，积分方程方法，混合方法。然后深入论述基函数以及矩量法。最后，将传统的积分方程方法与模式匹配方法相结合，建立了波导馈电的腔体问题的等效模型。
通过研究波导的等效模型，获得了对波导馈电的电大尺寸复杂结构激励、传输与辐射的高效数值求解策略。本文研究了波导馈电的电大尺寸结构（包括金属、金属-介质混合结构的波束波导、多波导端口辐射器）的传输和辐射问题的精确电磁建模与高效计算的数值方法，并选用多层快速多极子算法进行快速求解。
使用上述方法仅需对待求结构中的金属表面和介质体区域进行离散。而通常的波束波导恰好具有电大尺寸的金属表面和大量的无需剖分的空域，这使得采用积分方程方法与采用微分方程方法相比，极大地降低了未知量，提高了求解效率。使用波导模式匹配方法，考虑各导波模式的反射影响，可得到激励口面处的场匹配状况，并最终获得精确的场解。
在此基础上，对上述方法进行扩展后可对多波导端口馈电的天线阵列给出精确的场解。当这种天线阵列的阵元数目增多，整体电尺寸变大，且阵列中可能存在不同结构的阵元，其间又存在复杂的电磁耦合。这导致数值仿真需要耗费大量的计算资源，甚至无法计算。本论文提供的等效模型和高效算法则可求解多个馈源、各个馈源可具任意形态和结构、各个辐射结构可具任意的馈电模式、各馈源间可有任意的相对位置的传输与辐射问题。
为进一步提高对电大尺寸波束波导传输特性的求解效率，采用了相位提取(PE)基函数来描述电流。这样做的根据是波束波导内部金属表面上的感应电流在入射波方向上呈周期性变化。与传统的基函数比较而言，PE基函数可以被定义在更大的贴片上。使用PE基函数直接地减少了待求未知量，极大地增强了求解电大尺寸波束波导问题的能力。
在迭代求解过程中，成功的将预条件方法应用到本文方法中，得到了显著的效果。此外，本文研究的算法在结合OpenMP并行计算技术之后，计算能力得到了大幅的提升。作者依据本文方法开发完成了相应的数值仿真程序，并得到了数值算例的验证。
The accurate modeling and efficient solving of the beam waveguide(BWG)transmission system is always a challenge in the computational electromagnetics. Thebeam waveguide always has large size compared with the wavelength, complexstructure, and composite metallic-material structure. It cause the huge computation loadand the slow iteration process. In this thesis, the integral equation(IE) method and themode matching(MM) method are combined together to simplify the model, and thepreconditioning technique is used to accelerate the convergence speed. To deal with thestructure of electrically large size, the multilevel fast multipole algorithm(MLFMA) isused. Decomposing the free space Green’s function by the style of aggregation,transformation and disaggregation, MLFMA successfully reduces the computationcomplexity to O (N log N). The transmission problems of beam waveguide withelectronically large size and complex structure can be solved efficiently by using thisintegrated modelling and simulation environment. The characteristics of reflectors withany number, arbitrary shape, and arbitrary position while illuminated by the horn feedcan be solved efficiently. In practical application, the method mentioned above can beused to obtain the radiation and scattering characteristics of the radomes, the frequencyselective surfaces, and the large side-fed reflector antennas efficiently.
First, the traditional numerical methods of solving the excitation, transmission andradiation problems of the complex structure are introduced. Including the analyticalmethod, the high-frequency method, the differential equation method, the integralequation method and the hybrid method. The basis functions and the method of momentare deeply studyed. Finally, the integral equation method is combined with the modematching method and the equivalent model of the waveguide-fed cavities.
By studying the equivalent model of the waveguide, we got the efficient numericalmethod of solving the excitation, transmission and radiation problems of theelectrically-large and complex beam waveguide structures. We have discussed theaccurate modeling and effective numerical solving of the transmission and radiation ofthe waveguide-fed electrically-large structure problems(including the conductor or thecomposite metallic-material beam waveguide and the arbitrary multi-port radiation structures). Then the MLFMA is used to improve the efficiency of the solving process.
Using the integral equation method, we only need to discrete the surface of the ideaconductor and the volume of the dielectric area. The characteristic of the beamwaveguide always contains large space without any PEC or volumn structure. Then thenumber of unknowns is much less and the solving efficiency is much higher comparedby using the differential equation methods. Using the mode matching method, andconsidering the reflecting guide wave modes, we can get the matching situation on theexciting erea and the accurate results.
The method of dealing with the single waveguide-fed problem is expanded tosimulate the multi-port waveguide-fed antenna array problems. The increasing numberof antenna elements brings the large electrical size. And there are always the elementswith different structure and feeding mode and the complex electromagnetic coupling.The requirement of computing resource is great, which even cannot be supplied. Themodel and efficient algorithm raised in this thesis can deal with the multi-portwaveguide-fed transmission and radiation problems with feeds of arbitrary amount,structure, excitation mode and relative position.
In order to further improve the efficient of solving the transmission problems of thebeam waveguide with electrically large size structure, we used the phase-extracted(PE)basis functions to describe the surface electric current. The reason is that the phase ofthe electric induced current on the PEC surface of the beam waveguide changeperiodically along the direction of the incident wave. Comparing with the traditionalbasis functions, the PE basis function can be defined on the larger patches. Using thisbasis function, the unknowns is directly reduced and the ability of solving the beamwaveguide with electronically large size is greatly improved.
In the solving process, the preconditioning technique is used, and the better effectis got. Moreover, the OpenMP parallel technique is adopted and the solving efficiency isgreatly improved. The author has been developed the program codes based on themethods mentioned in this dissertation, which is validated by the numerical experiment.
引文
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