旋转对称频域和时域积分方程方法及其软件实现和应用
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摘要
利用轴对称性可以将电大的旋转对称体电磁问题转化为求解一组具有小规模矩阵方程的问题(每个具有小规模矩阵方程的问题称为原问题的Fourier分量或模式),从而大大提高计算效率,减少内存需求。本论文从频域和时域积分方程方法两个角度研究了旋转对称体的散射和辐射特性。所做的工作概述如下:
频域方面,采用多种基函数,深入研究了旋转对称导体、介质体和涂覆体以及较复杂的多区域问题和手征媒质等,并对影响旋转对称矩量法效率和稳定性的关键技术作了较大改进,主要包括
·提出了一种精度可控的模式数截断方法:斜入射激励的旋转对称体,需要多个Fourier分量的叠加。该方法通过一个称为部分迭代的过程截取达到所需电流精度的最少模式数。其迭代过程的收敛判据由模式电流(各Fourier模式对应的电流)沿母线的分布规律而得,几乎不付代价。
·基于积分核的谱估计和Filon算法,我们提出了一种准自适应积分方法用于高效、稳定计算模式格林函数(BoR问题专有的格林函数)的急速振荡积分:该方法可以根据场源点的几何位置参数,自适应地选择积分区间[0,π]内Gauss积分的采样点数,在保持很高计算精度的前提下,具有自适应、高效(比基于Filon算法的分段自适应方法提高1个数量级左右)和稳定的优点。
·提出了模式缩减技术:该技术根据模式格林函数的幅度随模式增加的分布规律,认为随着模式序号的增加,阻抗矩阵的部分元素小到可以直接置0。我们用一个截断公式来确定当前模式真正需要填充的矩阵元素,将高次模式的计算效率提高了1～3个数量级。
·提出了近轴-远距模式格林函数的解析表达式:该表达式将BoR问题的计算效率提高了1～6倍,特别适合细长旋转对称体,如导弹、线天线等的快速计算。
·基于高阶阻抗边界条件(HOIBC)的局部性和MIE级数解的实时性,提出了一种切实可行的HOIBC适用性验证办法:将特殊形体的MIE级数解和HOIBC结合,并将其代码嵌入软件以实时验证当前涂覆是否可以用HOIBC近似。该验证过程几乎不花费时间。
在时域方面,提出并实现了基于阶数步进(MoD)的旋转对称时域积分方程方法。相比基于时间步进(MoT)的BoR算法,该方法真正利用了旋转对称体的轴对称特性并继承了普通MoD法精度高,后期无条件稳定的优点。与没有利用轴对称性的普通MoD法和普通MoT法相比,该方法在计算效率上提高了2个数量级以上。
完成了基于频域旋转对称矩量法(BoRFDMoM)的软件BoRMoMModeler1.0;2.0版本的核心代码也已完成,包括时域积分方程方法和改进后更高效稳定,适用于更多计算对象的频域方法。
在应用方面,BoRMoMModeler1.0已交用户用于雷达目标散射特性建模,反映良好;在本课题组,我们用BoRMoM设计旋转对称天线:对一个带天线罩和齿槽的空心波束天线进行一体化优化设计,其性能很好得满足了用户要求。
The usage of the axisymmetric property of the bodies of revolution (BoR) can convert an original electrically large BoR-problem into a series problems with small size of matrix equations, which can greatly reduce the computational cost and we call each small problem a Fourier component or mode of the original one. This dissertation is focused on both the frequency and time domain integral equation methods for computing the scattering and radiation property of the bodies of revolution. What we have done are listed below:
In frequency domain, several basis functions are applied to investigate the scattering and radiation property of the bodies of revolution, including perfectly electric conducting objects, dielectric objects, coated objects, more complex muti-region objects and chiral media, etc.. Several key points which can greatly affect the efficiency and robustness of the moment method for bodies of revolution (BoRMoM) are investigated. The method are greatly improved by several new techniques, which include:
An accuracy controllable method has been proposed to truncate the number of Fourier components when the plane wave incidents obliquely, which we call a partly iterative method. One can get the least number of Fourier components required for a given accuracy of the currents. A costless convergence criteria is proposed by investigating the distribution property of the mode currents (currents corresponding to each Fourier component) along the generating curve.
The computation of the modal Green's function forms a bottleneck to further enhance the efficiency and robustness of the BoRMoM. Based on a spectrum estimation, a qusi-adaptive integral scheme is proposed to fast compute a group of extremely oscillating integrals of the modal Green's function (a special Green's function for the BoR-problems). It is based on the Filon algorithm and a formulation is derived to smartly determine the required number of sampling points for applying Gaussian quadrature in the whole range of [0,π] along the circumferential direction. Source and field points with different geometric parameters have different number of sampling points. This method is smart, fast, robust and still of high accuracy.
A mode reduction technique is proposed to enhance the computational efficiency of high order Fourier components. We found that, as the index of the mode increases, some elements of the impedance matrix are neglegible. A formulation is proposed to determine whether an element of the impedance matrix can be set as zero directly.
A closed form expressions for near-axis, far-distance modal Green's functions are proposed, which can be used to accelerate the computation of the BoR-problems especially when the BoR is slim.
A good method is proposed to verify whether the higher order impedance boundary condition (HOIBC) can be applied to a coated BoR. Based on the local property of the HOIBC and the costless of the MIE series solution, the method applies HOIBC in the MIE series solution for several special objects, e.g. sphere, and embeds the program into the software, which can be run for verification before the application of HOIBC to the coated BoR. The procedure for verification is costless.
In time domain, a marching-on-in-degree (MoD) procedure based time-domain integral equation method has been proposed for solving BoR-problems. Compared with the previous work based on a marching-on-in-time (MoT) procedure, this method can not only utilize the symmetric property of BoR indeed, but also retain the stable property of the common MoD method. Compared with the MoD method without using the symmetric property and the conventional MoT method, it can significantly enhance the computational efficiency.
A software BoRMoMModeler1.0 has been developed based on the frequency domain method (BoRFDMoM). The kernel of version 2.0 has also been finished which includes time domain integral equation methods and a more efficient and robust frequency domain method with more wide range of utility.
The software BoRMoMModeler1.0 has been applied to model the electromagnetic scattering from the radar targets by the users. In our own group, a horn antenna with ripples and airborne radome are optimized as a whole to obtain a special radiation pattern which we call hollow beam. All its performances can answer to the requirements.
频域方面,采用多种基函数,深入研究了旋转对称导体、介质体和涂覆体以及较复杂的多区域问题和手征媒质等,并对影响旋转对称矩量法效率和稳定性的关键技术作了较大改进,主要包括
·提出了一种精度可控的模式数截断方法:斜入射激励的旋转对称体,需要多个Fourier分量的叠加。该方法通过一个称为部分迭代的过程截取达到所需电流精度的最少模式数。其迭代过程的收敛判据由模式电流(各Fourier模式对应的电流)沿母线的分布规律而得,几乎不付代价。
·基于积分核的谱估计和Filon算法,我们提出了一种准自适应积分方法用于高效、稳定计算模式格林函数(BoR问题专有的格林函数)的急速振荡积分:该方法可以根据场源点的几何位置参数,自适应地选择积分区间[0,π]内Gauss积分的采样点数,在保持很高计算精度的前提下,具有自适应、高效(比基于Filon算法的分段自适应方法提高1个数量级左右)和稳定的优点。
·提出了模式缩减技术:该技术根据模式格林函数的幅度随模式增加的分布规律,认为随着模式序号的增加,阻抗矩阵的部分元素小到可以直接置0。我们用一个截断公式来确定当前模式真正需要填充的矩阵元素,将高次模式的计算效率提高了1～3个数量级。
·提出了近轴-远距模式格林函数的解析表达式:该表达式将BoR问题的计算效率提高了1～6倍,特别适合细长旋转对称体,如导弹、线天线等的快速计算。
·基于高阶阻抗边界条件(HOIBC)的局部性和MIE级数解的实时性,提出了一种切实可行的HOIBC适用性验证办法:将特殊形体的MIE级数解和HOIBC结合,并将其代码嵌入软件以实时验证当前涂覆是否可以用HOIBC近似。该验证过程几乎不花费时间。
在时域方面,提出并实现了基于阶数步进(MoD)的旋转对称时域积分方程方法。相比基于时间步进(MoT)的BoR算法,该方法真正利用了旋转对称体的轴对称特性并继承了普通MoD法精度高,后期无条件稳定的优点。与没有利用轴对称性的普通MoD法和普通MoT法相比,该方法在计算效率上提高了2个数量级以上。
完成了基于频域旋转对称矩量法(BoRFDMoM)的软件BoRMoMModeler1.0;2.0版本的核心代码也已完成,包括时域积分方程方法和改进后更高效稳定,适用于更多计算对象的频域方法。
在应用方面,BoRMoMModeler1.0已交用户用于雷达目标散射特性建模,反映良好;在本课题组,我们用BoRMoM设计旋转对称天线:对一个带天线罩和齿槽的空心波束天线进行一体化优化设计,其性能很好得满足了用户要求。
The usage of the axisymmetric property of the bodies of revolution (BoR) can convert an original electrically large BoR-problem into a series problems with small size of matrix equations, which can greatly reduce the computational cost and we call each small problem a Fourier component or mode of the original one. This dissertation is focused on both the frequency and time domain integral equation methods for computing the scattering and radiation property of the bodies of revolution. What we have done are listed below:
In frequency domain, several basis functions are applied to investigate the scattering and radiation property of the bodies of revolution, including perfectly electric conducting objects, dielectric objects, coated objects, more complex muti-region objects and chiral media, etc.. Several key points which can greatly affect the efficiency and robustness of the moment method for bodies of revolution (BoRMoM) are investigated. The method are greatly improved by several new techniques, which include:
An accuracy controllable method has been proposed to truncate the number of Fourier components when the plane wave incidents obliquely, which we call a partly iterative method. One can get the least number of Fourier components required for a given accuracy of the currents. A costless convergence criteria is proposed by investigating the distribution property of the mode currents (currents corresponding to each Fourier component) along the generating curve.
The computation of the modal Green's function forms a bottleneck to further enhance the efficiency and robustness of the BoRMoM. Based on a spectrum estimation, a qusi-adaptive integral scheme is proposed to fast compute a group of extremely oscillating integrals of the modal Green's function (a special Green's function for the BoR-problems). It is based on the Filon algorithm and a formulation is derived to smartly determine the required number of sampling points for applying Gaussian quadrature in the whole range of [0,π] along the circumferential direction. Source and field points with different geometric parameters have different number of sampling points. This method is smart, fast, robust and still of high accuracy.
A mode reduction technique is proposed to enhance the computational efficiency of high order Fourier components. We found that, as the index of the mode increases, some elements of the impedance matrix are neglegible. A formulation is proposed to determine whether an element of the impedance matrix can be set as zero directly.
A closed form expressions for near-axis, far-distance modal Green's functions are proposed, which can be used to accelerate the computation of the BoR-problems especially when the BoR is slim.
A good method is proposed to verify whether the higher order impedance boundary condition (HOIBC) can be applied to a coated BoR. Based on the local property of the HOIBC and the costless of the MIE series solution, the method applies HOIBC in the MIE series solution for several special objects, e.g. sphere, and embeds the program into the software, which can be run for verification before the application of HOIBC to the coated BoR. The procedure for verification is costless.
In time domain, a marching-on-in-degree (MoD) procedure based time-domain integral equation method has been proposed for solving BoR-problems. Compared with the previous work based on a marching-on-in-time (MoT) procedure, this method can not only utilize the symmetric property of BoR indeed, but also retain the stable property of the common MoD method. Compared with the MoD method without using the symmetric property and the conventional MoT method, it can significantly enhance the computational efficiency.
A software BoRMoMModeler1.0 has been developed based on the frequency domain method (BoRFDMoM). The kernel of version 2.0 has also been finished which includes time domain integral equation methods and a more efficient and robust frequency domain method with more wide range of utility.
The software BoRMoMModeler1.0 has been applied to model the electromagnetic scattering from the radar targets by the users. In our own group, a horn antenna with ripples and airborne radome are optimized as a whole to obtain a special radiation pattern which we call hollow beam. All its performances can answer to the requirements.
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