旋转结构体电磁问题的高效分析与应用
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摘要
随着计算机技术和电磁学的飞速发展,如何精确快速计算目标的电磁特性成为在目标识别、隐身与反隐身、微波成像等领域研究的重点。对于某些特殊结构,例如旋转体结构(BOR),由于几何外形的特性,对场进行傅立叶展开成不同模式的叠加,不同的模式由于模式正交特性可以独立讨论。传统的三维电磁问题可以退化为二维半问题,大大降低计算规模。本文研究的是基于旋转体结构的高效计算方法,主要分为五个部分讨论。
第一部分回顾了矩量法(MoM)计算旋转体结构目标的散射场,采用了三角基函数、脉冲基函数离散目标表面的等效电流和磁流。分别利用电场积分方程(EFIE)、磁场积分方程(MFIE)、混合积分方程(CFIE)计算理想导电(PEC)旋转体的雷达散射截面(RCS)。采用Poggio-Miller-Chang-Harrington-W(uPMCHW)方程分析均匀介质旋转体的RCS。最后,在理想导电体区域采用EFIE,在均匀介质区域采用PMCHW方程,分析了介质金属复合结构的电磁散射问题。
第二部分研究了快速非均匀平面波算法(FIPWA)求解电大尺寸的旋转体结构散射问题。采用Weyl恒等式展开格林函数,近场区仍然使用传统矩量法计算,当场源点满足远场关系,采用FIPWA技术。同时利用贝塞尔函数的解析积分表达,导出了旋转体结构聚合因子和配置因子的解析表达。采用FIPWA对旋转体结构进行电磁计算,大大降低了计算复杂度和内存需求复杂度,因此该方法特别适合电大尺寸的旋转体问题求解。
第三部分采用有限元方法(FEM)分析了复杂介质填充旋转腔体问题,该腔体内部介质在周向均匀,在截面上非均匀分布。本文采用三角形网格离散旋转体结构的截面,使用标量点元基函数和矢量边元基函数分别表示不同模式下周向和切向场分量。分析了腔体内部的不同谐振模式的谐振频率、场分布等问题。利用不同的基函数组合,抑制奇异模出现。在此基础上,又采用了高阶有限元分析了旋转结构腔体问题,提高了计算的精度。
第四部分结合有限元方法和边界元方法处理任意截面非均匀介质分布的旋转结构目标的散射问题。将计算区域分为内部区域和外部区域,内部区域的场采用有限元方法计算,外部区域采用积分方程计算表面等效电流和磁流的关系。结合有限元方法和边界元方法计算,该算法既可以方便处理非均匀介质分布,保持了算法的灵活性;同时无需添加吸收边界条件,利用格林函数直接满足辐射条件,又保证了结果的精确性。该方法也可用于介质金属复合结构的电磁散射问题。第五部分采用多区迭代方法分析群旋转体目标。将每一个旋转体目标单独划分为一个子域求解,逐渐考虑子域之间的耦合,直到最后整体解收敛,子域之间的耦合和子域内部耦合都采用多层快速多极子求解。同时在这个基础上,采用多区迭代方法分析了任意三维结构的多体目标和电大尺寸目标,既保证了求解的精度,同时也很好的节约了计算资源。
本文采用积分方程方法,有限元方法,有限元-边界元混合方法分析旋转体结构目标。通过快速算法加速计算,节约计算资源。本文的研究工作表明,快速高效的算法能够很好的提高旋转体结构目标问题的求解效率,在实际电子工程中有极大优势。
With the development of computer science and electromagnetics, accurate and fast computational electromagnetics is an important topic in many areas, such as recognizing the target, stealth and anti-stealth technology, micro-wave imaging. The field of some spectial geometry like body of revolution (BOR) can be expressed in a Fourier series because of the axial symmetry of the geometry. The computational complesity is reduced because of the orthogonality of each mode. The 3-D domain is reduced to 2.5-D which will depress the scale of electromagnetic computation. The thesis mainly concentrates on the fast and efficient algorithm based on body of revolution. And it contains five parts as follows.
The method of moments (MoM) for scattering problem of body of revolution is reviewed in the first part. Triangular basis and pluse basis are used to expand the equivalent electric and magnetic currents. Electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) are used for solving perfect electric conductor (PEC) BOR's radar cross section (RCS). Poggio-Miller-Chang-Harrington-Wu(PMCHW)equation is implemented to analyze homogeneous BOR's problems. Composite BOR is then simulated with EFIE in PEC region and PMCHW equation in dielectic region.
Fast inhomogeneous plane wave algorithm (FIPWA) is introduced for BOR’s scattering prolem in the second part. The Green's function is expanded in inhomogeneous plane waves by using Weyl identity. Traditional MoM is used for near field part. FIPWA is used for far field interaction. Using the integral expression of Bessel function, the aggregation and disaggregation factors can be expressed in analytical form. The memory requirment and CPU time are saved by using FIPWA for scattering problems of large scale BOR.
A finite element method (FEM) with hybrid nodal and edge basis functions for solving nonaxisymmetric modes in axisymmetric resonators filled with inhomogeneous media is presented. The material is inhomogeneous on the cross section of the cavity. Non-zero eigenvalues can be reduced by choosing proper basis functions. Higher-order basis functions are used to improve the accuracy with the same number of unknowns.
FEM and boundary integration (BI) method are combined for solving the scattering problem of imhomogeneous BOR in the forth part. FEM is used for solving the inhomogeneous interior region with nodal and edge basis functions. BI is used for solving the exterior region part. This hybrid algorithm takes the advantages of FEM and BI. It can handle inhomogeneous problem efficiently and guarantee the accuracy at the same time.
Muiti-region iteration (MRI) is used for solving multi-BOR problems in the last part. Each BOR is set as one region and solved independently. The coupling is considered during the iteration. Large scale 3-D PEC objects or multi-objects with arbitrary shape are also simulated by proposed MRI. The memory requirement is saved and the accuracy is guaranteed at the same time.
Integral equation (IE), FEM, higher-order FEM and FEM-BI are studied for BOR problem in the thesis. The efficienncy and accuracy are improved by using these different methods. The studies of this thesis demonstrate that fast and efficient algorithm for BOR can be used to improve the efficiency and accuracy and will be extended in future research and engineering application.
第一部分回顾了矩量法(MoM)计算旋转体结构目标的散射场,采用了三角基函数、脉冲基函数离散目标表面的等效电流和磁流。分别利用电场积分方程(EFIE)、磁场积分方程(MFIE)、混合积分方程(CFIE)计算理想导电(PEC)旋转体的雷达散射截面(RCS)。采用Poggio-Miller-Chang-Harrington-W(uPMCHW)方程分析均匀介质旋转体的RCS。最后,在理想导电体区域采用EFIE,在均匀介质区域采用PMCHW方程,分析了介质金属复合结构的电磁散射问题。
第二部分研究了快速非均匀平面波算法(FIPWA)求解电大尺寸的旋转体结构散射问题。采用Weyl恒等式展开格林函数,近场区仍然使用传统矩量法计算,当场源点满足远场关系,采用FIPWA技术。同时利用贝塞尔函数的解析积分表达,导出了旋转体结构聚合因子和配置因子的解析表达。采用FIPWA对旋转体结构进行电磁计算,大大降低了计算复杂度和内存需求复杂度,因此该方法特别适合电大尺寸的旋转体问题求解。
第三部分采用有限元方法(FEM)分析了复杂介质填充旋转腔体问题,该腔体内部介质在周向均匀,在截面上非均匀分布。本文采用三角形网格离散旋转体结构的截面,使用标量点元基函数和矢量边元基函数分别表示不同模式下周向和切向场分量。分析了腔体内部的不同谐振模式的谐振频率、场分布等问题。利用不同的基函数组合,抑制奇异模出现。在此基础上,又采用了高阶有限元分析了旋转结构腔体问题,提高了计算的精度。
第四部分结合有限元方法和边界元方法处理任意截面非均匀介质分布的旋转结构目标的散射问题。将计算区域分为内部区域和外部区域,内部区域的场采用有限元方法计算,外部区域采用积分方程计算表面等效电流和磁流的关系。结合有限元方法和边界元方法计算,该算法既可以方便处理非均匀介质分布,保持了算法的灵活性;同时无需添加吸收边界条件,利用格林函数直接满足辐射条件,又保证了结果的精确性。该方法也可用于介质金属复合结构的电磁散射问题。第五部分采用多区迭代方法分析群旋转体目标。将每一个旋转体目标单独划分为一个子域求解,逐渐考虑子域之间的耦合,直到最后整体解收敛,子域之间的耦合和子域内部耦合都采用多层快速多极子求解。同时在这个基础上,采用多区迭代方法分析了任意三维结构的多体目标和电大尺寸目标,既保证了求解的精度,同时也很好的节约了计算资源。
本文采用积分方程方法,有限元方法,有限元-边界元混合方法分析旋转体结构目标。通过快速算法加速计算,节约计算资源。本文的研究工作表明,快速高效的算法能够很好的提高旋转体结构目标问题的求解效率,在实际电子工程中有极大优势。
With the development of computer science and electromagnetics, accurate and fast computational electromagnetics is an important topic in many areas, such as recognizing the target, stealth and anti-stealth technology, micro-wave imaging. The field of some spectial geometry like body of revolution (BOR) can be expressed in a Fourier series because of the axial symmetry of the geometry. The computational complesity is reduced because of the orthogonality of each mode. The 3-D domain is reduced to 2.5-D which will depress the scale of electromagnetic computation. The thesis mainly concentrates on the fast and efficient algorithm based on body of revolution. And it contains five parts as follows.
The method of moments (MoM) for scattering problem of body of revolution is reviewed in the first part. Triangular basis and pluse basis are used to expand the equivalent electric and magnetic currents. Electric field integral equation (EFIE), magnetic field integral equation (MFIE) and combined field integral equation (CFIE) are used for solving perfect electric conductor (PEC) BOR's radar cross section (RCS). Poggio-Miller-Chang-Harrington-Wu(PMCHW)equation is implemented to analyze homogeneous BOR's problems. Composite BOR is then simulated with EFIE in PEC region and PMCHW equation in dielectic region.
Fast inhomogeneous plane wave algorithm (FIPWA) is introduced for BOR’s scattering prolem in the second part. The Green's function is expanded in inhomogeneous plane waves by using Weyl identity. Traditional MoM is used for near field part. FIPWA is used for far field interaction. Using the integral expression of Bessel function, the aggregation and disaggregation factors can be expressed in analytical form. The memory requirment and CPU time are saved by using FIPWA for scattering problems of large scale BOR.
A finite element method (FEM) with hybrid nodal and edge basis functions for solving nonaxisymmetric modes in axisymmetric resonators filled with inhomogeneous media is presented. The material is inhomogeneous on the cross section of the cavity. Non-zero eigenvalues can be reduced by choosing proper basis functions. Higher-order basis functions are used to improve the accuracy with the same number of unknowns.
FEM and boundary integration (BI) method are combined for solving the scattering problem of imhomogeneous BOR in the forth part. FEM is used for solving the inhomogeneous interior region with nodal and edge basis functions. BI is used for solving the exterior region part. This hybrid algorithm takes the advantages of FEM and BI. It can handle inhomogeneous problem efficiently and guarantee the accuracy at the same time.
Muiti-region iteration (MRI) is used for solving multi-BOR problems in the last part. Each BOR is set as one region and solved independently. The coupling is considered during the iteration. Large scale 3-D PEC objects or multi-objects with arbitrary shape are also simulated by proposed MRI. The memory requirement is saved and the accuracy is guaranteed at the same time.
Integral equation (IE), FEM, higher-order FEM and FEM-BI are studied for BOR problem in the thesis. The efficienncy and accuracy are improved by using these different methods. The studies of this thesis demonstrate that fast and efficient algorithm for BOR can be used to improve the efficiency and accuracy and will be extended in future research and engineering application.
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