基于特征基函数的高效算法及其在电磁散射中的应用
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摘要
随着航空、航天、航海等电子技术的发展,在雷达目标隐身和反隐身技术、雷达目标特征分析以及现代电子系统中的电磁兼容性等领域经常需要对一些具有复杂结构的三维目标体做电磁建模,并力求精准且快速的分析结果,这一需求也成为了计算电磁学领域的研究热点。本文在此背景下对计算电磁学中的一个分支进行了研究,以表面积分方程为理论基础,通过矩量法的求解方式,提出了一种新的计算方法——自适应修正特征基函数法。整篇文章紧紧围绕这一新的方法,研究该方法的加速技术以及对不同类型目标体电磁散射分析的适应性,最终的目的是通过开发通用的电磁计算程序来切实可行的解决电磁工程中复杂的电磁目标特性。本文中,对该方法的研究主要分为两大部分,第一部分是方法本身的研究,包括方法的提出,加速技术等,第二部分是方法的拓展,包括将自适应修正特征基函数法应用到均匀介质体、介质与理想导体混合体的电磁散射研究中,并详细讨论了该方法在windows环境下的并行实现等。
在第一部分中,首先提出了一种新的计算方法——自适应修正特征基函数法(AMCBFM),该方法对目标体的阻抗矩阵进行分块,通过等效电流或者磁流系数的自适应修正技术,克服了已有方法中对基函数阶数的选取不能自由控制的缺点,采用一种简单的电流误差判断方式方便快捷地控制计算精度。并讨论了不同参数,包括分块数目、基函数阶数等对计算效率的影响,找出了较为合适的取值,数值结果表明本方法具有较高的计算效率。在此基础上,将基于Dual-MGS的QR分解技术与AMCBFM结合,通过判断块间互阻抗矩阵的数值秩来确定是否进一步计算其他块间互阻抗矩阵,大大降低了内存需求,提高了计算速度。同时,将基于MBPE的有理函数插值技术与AMCBFM结合,成功的应用到了电大尺寸目标体的单站RCS求解以及宽带特性研究中,讨论了部分参数比如第三采样点、精度误差、分段采样等对计算效率的影响,数值结果表明采用该插值方法后,所需要的采样点数目大大减少。
在第二部分中,主要围绕AMCBFM进行拓展研究。首先简单介绍了适用于均匀介质体的PMCHW方程组,该方程组基于场等效性原理和表面积分方程。与AMCBFM结合,用来分析均匀介质体的电磁散射,讨论了块间重叠区域、基函数阶数的选取等对计算效率的影响。建立了用于介质与理想导体混合体的表面积分方程组EFIE-PMCHW,与AMCBFM结合,分析了完全涂敷介质的理想导体,部分涂敷介质的理想导体等目标体的电磁散射问题,讨论了介质厚度,介电常数等参数对计算效率的影响,通过分析微带天线、微带天线阵等目标体的电磁散射进一步验证了方法的正确性和高效性。最后,在windows环境下,实现了AMCBFM方法的并行运算,采用动静态结合负载平衡的并行方式,克服了在静态负载平衡并行算法中由于不同类型计算机节点处理数据的效率不同而导致计算效率低下的缺点,同时具备了动态负载平衡算法的灵活性。通过QR-AMCBFM实行并行技术后,进一步提高了计算效率,本文亦实现了介质与理想导体混合体电磁散射的并行计算,结果显示对于处理更大电尺寸的目标体电磁散射问题具有很好的适用性。
With the development of electronic technologies for aeronautics, astronautics and navigation, the techniques of radar target stealth and anti-stealth, RCS and electromagnetic compatibility are required for accurate analysis on 3-D objects with complex structures. Because of the request, this is becoming a hot topic in electromagnetic field. In this dissertation, the research on one branch of computational electromagnetic has been studied. Based on the surface integral equations expanded by moment method, a new method called adaptively modified characteristic basis function method (AMCBFM) is proposed. The whole study clue is based on this method in order to seek one effective approach to analyze the electromagnetic characteristic of some intricate targets. The universal programs and accelerative technologies are required to slove the complex electromagnetic characteristics of different oblects.
This dissertation includes two aspects in principle. One part is the study on the new method, including its principium and related accelerative technologies, and the other part is the applications for analyzing electromagnetic scattering problems on homogeneous dielectric objects as well as mixed homogeneous dielectric and PEC objects. The parallel algorithm executed in windows environment is also discussed.
In the first portion, the AMCBFM is proposed. This method divides the studied objects into many blocks and uses an adaptively modified technique to overcome the shortcoming which is not convenient to choose the levels of characteristic basis functions (CBFs) in the conventional characteristic basis function methods (CBFMs). And a simple way is applied to control the current error precision. Some different parameters including the number of blocks and the levels of CBFs are discussed to find out the effect on the computational efficiency, and the appropriate values are turned up. The results from the method agree well with that from the conventional methods. Subsequently, the QR factorization based on Dual-MGS is combined with AMCBFM to reduce the RAM storage and improve the computational speed. Moreover, it is successful to use the model based parameters estimation (MBPE) technology and AMCBFM in analyzing the monostatic RCS and wideband response of large electric objects. And the influence of several parameters on the results, such as the third sampling point, precision error and subsection sampling, is discussed and it shows that the number of sampling points reduces sharply.
In the second portion, the studies on the further application of AMCBFM are carried out. The PMCHW equations for homogenous dielectric objects are reviewed, which are based on the equivalent principles and surface integral equations. After combined with AMCBFM, the new method, PMCHW-AMCBFM, is proposed. Moreover, the overlap domain between adjacent blocks and the levels of CBFs are also investigated to seek the suitable values. Subsequently, the surface integral equations, EFIE-PMCHW, for the electromagnetic scattering problem of mixed homogenous dielectric and PEC objects are introduced and combined with AMCBFM triumphantly called as EFIE-PMCHW-AMCBFM. And the electromagnetic scattering of microstrip antennas and microstrip antenna arrays are analyzed accurately, which validates the validity and veracity of this method. At last, the dynamic-static load balance parallel algorithm based on AMCBFM is executed in windows environment. This algorithm overcomes the disadvantages of static load balance parallel algorithm and has the advantages of dynamic load balance parallel algorithm. And the algorithm combined with QR-AMCBFM and EFIE-PMCHW-AMCBFM is implemented to solve the electromagnetic scattering problems aroused by various large electric objects effectively.
在第一部分中,首先提出了一种新的计算方法——自适应修正特征基函数法(AMCBFM),该方法对目标体的阻抗矩阵进行分块,通过等效电流或者磁流系数的自适应修正技术,克服了已有方法中对基函数阶数的选取不能自由控制的缺点,采用一种简单的电流误差判断方式方便快捷地控制计算精度。并讨论了不同参数,包括分块数目、基函数阶数等对计算效率的影响,找出了较为合适的取值,数值结果表明本方法具有较高的计算效率。在此基础上,将基于Dual-MGS的QR分解技术与AMCBFM结合,通过判断块间互阻抗矩阵的数值秩来确定是否进一步计算其他块间互阻抗矩阵,大大降低了内存需求,提高了计算速度。同时,将基于MBPE的有理函数插值技术与AMCBFM结合,成功的应用到了电大尺寸目标体的单站RCS求解以及宽带特性研究中,讨论了部分参数比如第三采样点、精度误差、分段采样等对计算效率的影响,数值结果表明采用该插值方法后,所需要的采样点数目大大减少。
在第二部分中,主要围绕AMCBFM进行拓展研究。首先简单介绍了适用于均匀介质体的PMCHW方程组,该方程组基于场等效性原理和表面积分方程。与AMCBFM结合,用来分析均匀介质体的电磁散射,讨论了块间重叠区域、基函数阶数的选取等对计算效率的影响。建立了用于介质与理想导体混合体的表面积分方程组EFIE-PMCHW,与AMCBFM结合,分析了完全涂敷介质的理想导体,部分涂敷介质的理想导体等目标体的电磁散射问题,讨论了介质厚度,介电常数等参数对计算效率的影响,通过分析微带天线、微带天线阵等目标体的电磁散射进一步验证了方法的正确性和高效性。最后,在windows环境下,实现了AMCBFM方法的并行运算,采用动静态结合负载平衡的并行方式,克服了在静态负载平衡并行算法中由于不同类型计算机节点处理数据的效率不同而导致计算效率低下的缺点,同时具备了动态负载平衡算法的灵活性。通过QR-AMCBFM实行并行技术后,进一步提高了计算效率,本文亦实现了介质与理想导体混合体电磁散射的并行计算,结果显示对于处理更大电尺寸的目标体电磁散射问题具有很好的适用性。
With the development of electronic technologies for aeronautics, astronautics and navigation, the techniques of radar target stealth and anti-stealth, RCS and electromagnetic compatibility are required for accurate analysis on 3-D objects with complex structures. Because of the request, this is becoming a hot topic in electromagnetic field. In this dissertation, the research on one branch of computational electromagnetic has been studied. Based on the surface integral equations expanded by moment method, a new method called adaptively modified characteristic basis function method (AMCBFM) is proposed. The whole study clue is based on this method in order to seek one effective approach to analyze the electromagnetic characteristic of some intricate targets. The universal programs and accelerative technologies are required to slove the complex electromagnetic characteristics of different oblects.
This dissertation includes two aspects in principle. One part is the study on the new method, including its principium and related accelerative technologies, and the other part is the applications for analyzing electromagnetic scattering problems on homogeneous dielectric objects as well as mixed homogeneous dielectric and PEC objects. The parallel algorithm executed in windows environment is also discussed.
In the first portion, the AMCBFM is proposed. This method divides the studied objects into many blocks and uses an adaptively modified technique to overcome the shortcoming which is not convenient to choose the levels of characteristic basis functions (CBFs) in the conventional characteristic basis function methods (CBFMs). And a simple way is applied to control the current error precision. Some different parameters including the number of blocks and the levels of CBFs are discussed to find out the effect on the computational efficiency, and the appropriate values are turned up. The results from the method agree well with that from the conventional methods. Subsequently, the QR factorization based on Dual-MGS is combined with AMCBFM to reduce the RAM storage and improve the computational speed. Moreover, it is successful to use the model based parameters estimation (MBPE) technology and AMCBFM in analyzing the monostatic RCS and wideband response of large electric objects. And the influence of several parameters on the results, such as the third sampling point, precision error and subsection sampling, is discussed and it shows that the number of sampling points reduces sharply.
In the second portion, the studies on the further application of AMCBFM are carried out. The PMCHW equations for homogenous dielectric objects are reviewed, which are based on the equivalent principles and surface integral equations. After combined with AMCBFM, the new method, PMCHW-AMCBFM, is proposed. Moreover, the overlap domain between adjacent blocks and the levels of CBFs are also investigated to seek the suitable values. Subsequently, the surface integral equations, EFIE-PMCHW, for the electromagnetic scattering problem of mixed homogenous dielectric and PEC objects are introduced and combined with AMCBFM triumphantly called as EFIE-PMCHW-AMCBFM. And the electromagnetic scattering of microstrip antennas and microstrip antenna arrays are analyzed accurately, which validates the validity and veracity of this method. At last, the dynamic-static load balance parallel algorithm based on AMCBFM is executed in windows environment. This algorithm overcomes the disadvantages of static load balance parallel algorithm and has the advantages of dynamic load balance parallel algorithm. And the algorithm combined with QR-AMCBFM and EFIE-PMCHW-AMCBFM is implemented to solve the electromagnetic scattering problems aroused by various large electric objects effectively.
引文
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