【作者】 罗伟；

【导师】 尹文言；

【作者基本信息】 上海交通大学 ， 电磁场与微波技术， 2014， 博士

【摘要】 现代舰船上装备数量众多的电子信息设备,带来了许多电磁兼容和电磁干扰难题,而计算机仿真技术可以对舰船平台上一些电磁现象和电磁干扰的机理进行数值模拟。该论文对时域积分方程方法进行了较为深入、系统地研究,发展了稳定、高效的时域积分方程方法及其混合方法,研究了高功率电磁脉冲作用下一些大型平台,特别是舰船平台模型的时域响应特性。论文主要工作概述如下:(1)考虑到目标离散后产生的未知量数目急剧增多,基于时间步进算法求解时域电场积分方程的系数阻抗矩阵Z0的条件数快速增大;同时,迭代求解过程中算法的收敛性随之变差。为此,论文提出了Calderón预条件技术,研究了该技术在时域积分方程中的应用。通过Calderón预条件处理后得到的系数矩阵,其条件数不会随目标网格的剖分均匀性和剖分密度变化而变化,并且在迭代求解时具有很好的收敛特性。(2)针对时域积分方程的后时不稳定性问题,论文提出了两种改进方法:首先研究瞬态基函数的选取。由于类椭球波函数是一种时域跨度有限长的频域带限函数,特别适合用于带限函数的内插和外推运算,其截断误差以指数率形式衰减。因此,该类函数非常适合作为待求解电流的时域基函数。另一方面,在奇异积分求解时,采用一种新的奇异积分方法,对积分方程内、外两层四重积分进行处理,包括用于处理内层2-D奇异的径向积分法(Radial Integration Scheme)和外层2-D积分的被积函数平滑技术。与传统的高斯积分方法相比较,这种方法的精度和效率都大幅提升。(3)针对时域积分方程的计算效率问题,论文提出了时域自适应积分方法。通过将原始非均匀分布的空间基函数投影到规则网格点上,而网格点上的转移矩阵和电流向量的乘积运算可借助快速傅里叶变换(Fast Fourier Transform,FFT)和其逆变换(Inverse Fast Fourier Transform,IFFT)快速计算得到,再将计算结果进行插值即可得到原始基函数上的位势。对于准平面结构的计算,时域自适应积分方法的计算复杂度和内存需求分别为2(log())t s sO N N N和3/2()sO N,而在普通三维结构处理中,时域自适应积分方法的计算复杂度和内存需求分别为3/2 2(log())t s sO N N N和2()sO N。其中sN和tN分别为空间和时间基函数的自由度。(4)为了提高时域积分方程的计算效率,论文进一步研究了时域积分方程的并行实现技术。采用基于消息传递接口(Message Passing Interface:MPI)方式来实现,该方式是目前国际上最流行的并行编程环境之一。(5)提出了时域线面结合积分方程-时域物理光学混合方法,该方法能有效处理线天线与导体平台相结合的情形。此外,通过引入核外技术(OOC)以及后时稳定性的改善方法,提高了该混合方法在处理更为复杂电磁问题的求解能力。在该混合方法实施之前,需要对TDIE和TDPO区域进行划分:天线、线面结合处与其在理想导体平台的邻近一小块区域属于TDIE区,导体屏上的孔缝与其邻近区域同样划分至TDIE区,而理想导体平台和导体屏上的剩余区域则属于TDPO区。(6)提出了时域积分方程-时域物理光学-时域自适应积分方法(TDIE-TDPOTDAIM)。在新的混合方法中,使用一套规则网格同时覆盖TDIE和TDPO区。TDIE区的自作用、TDIE区对TDPO区以及TDPO区对TDIE区的互作用都用TDAIM快速计算得到。该混合方法的计算效率明显超过了单一方法的计算效率。更多还原

【Abstract】 It is well known that there are numerous electronic systems equipped on modern ship platforms, and they bring a lot of very challenging electromagnetic compatibility(EMC) and electromagnetic interference(EMI) problems. On the other hand, computer simulation technique has been successfully adopted and implemented for predicting the electromagnetic phenomena and the mechanism of EMI. This dissertation, based on our developed stable and efficient time domain integral equation(TDIE) method and its hybrid method, is devoted to analyzing the transient characteristics of some large scale platforms in the presence of high-power electromagnetic pulses(HP-EMP).The main contribution of this dissertation is summarized as follows:(1) As the number of unknowns generated by surface mesh increases, the condition number of the impedance matrix Z0 grows rapidly. Moreover, the convergence of the algorithm deteriorates. In this dissertation, the Calderón precondition technique is implemented in the TDIE method. By utilizing this technique, the condition number of the impedance matrix will not change greatly as the variation of the mesh uniformity and mesh density of the target. At the same time, an excellent convergence characteristic is also achieved.(2) In order to handle the late time instability of TDIE solver, we present two improved methods. One is the choice of the temporal basis function. The approximate prolate spheroidal wave functions(APSWFs) have a short temporal support and limited bandwidth. Based on these properties, APSWFs are suitable for the interpolation or extrapolation of a band-limited function with the error decreased exponentially. Thus, this temporal basis function is usually used for representing the induced transient currents on the PEC surface. On the other hand, a new integration approach for calculating the matrix elements is also presented, and it mainly consists of a radial integration scheme for handling weakly singular inner integrals combined with some new smoothing techniques for treating the outer surface integrals. In comparison with the conventional Gaussian quadrature rule, both the accuracy and efficiency of the new integration approach are improved greatly.(3) Time domain adaptive integral method(TDAIM) is proposed to improve the efficiency of the conventional TDIE method. All the primary spatial basis functions are locally projected onto the auxiliary grids. The multiplication of the propagation matrix and current vector on these grids can be calculated by using the fast fourier fransform(FFT) and the inverse fast fourier fransform(IFFT). Finally, the potential value on each primary basis function is obtained by interpolating these intermediate results. The proposed scheme has a computational complexity and memory requirement of 2( log())t s sO N N N and 3/ 2()sO N when applied to quasiplanar structures, and for general 3-D surfaces, they are of 3/ 2 2( log())t s sO N N N and 2()sO N. Here, Ns and Nt denote the number of spatial and temporal degrees of freedom, respectively.(4) In order to improve the computational efficiency of the TDIE method, we also develop the parallel version. The message passing interface(MPI) is implemented in the parallel TDIE, which is one of the most popular parallel programming environments.(5) A generalized mathematical procedure of hybrid TDIE-TDPO method is proposed, and in particular, the technique for handling the junction between the wire antenna and the PEC platform is implemented. Moreover, the out-of-core technique and the method that improves the instability have been integrated into this hybrid TDIE-TDPO method to enhance its capability for handling complex EM problems. In our analysis, the antenna, the wire-surface junction and the small part of the PEC platform in its vicinity are assigned to the TDIE region. The small part of the PEC screen in the vicinity of multiple apertures is also set to be in the TDIE region, and the remainders of the PEC platform and the PEC screen are assigned to the TDPO region.(6) An efficient solver that hybridizes the TDIE-TDPO and TDAIM is presented. In the hybrid scheme, the TDAIM method uses a single grid system that covers both the TDIE and TDPO regions. The interactions within the TDIE region, as well as from the TDIE to the TDPO region, and back, can be obtained by using TDAIM. The hybrid scheme is computationally far more efficient than its standalone constituents.更多还原