三维非均匀介质成像问题的区域分解方法

在利用数值方法分析非均匀介质问题时,容易生成大型系数矩阵,从而在求解时常常造成计算机内存不足或者计算时间过长。该文利用区域分解方法对三维非均匀介质成像问题进行分析,通过将求解区域划分为几个子区域,在子区域上以迭代求解子问题的方式解决以上问题。文中给出的迭代收敛速度曲线证明区域分解算法的收敛速度很快。该文对一些复杂的非均匀介质问题给出了模拟测量成像的结果。     

棱边元分区的区域分解算法及其在电磁问题中的应用

针对三维电磁问题,该文提出了采用非结构化网格剖分计算区域,并按单元进行区域划分的区域分解算法。将原求解区域划分为若干个不重叠的子区域,先通过求解容量矩阵获得子区域之间连接边界上的场值,再利用矢量有限元快速计算出每个子区域内部的场值,显著地降低了计算复杂度和存储量。通过引入预条件的Krylov子空间法求解容量矩阵方程,加速了收敛,进一步提高了效率。数值算例验证了该方法的准确性和有效性。     

基于改进快速子空间迭代跟踪的部分自适应STAP算法

针对部分空时自适应(STAP)处理的特征值分解(EVD)影响杂波抑制的实时处理性能,提出了基于改进快速子空间迭代跟踪(PAST)的部分自适应STAP算法.该方法首先在PAST处理的基础上,对正交PAST方法进行改进,得到改进后的PAST(MPAST)方法;然后将MPAST方法应用于计算部分自适应STAP算法的特征子空间,从而有效提高STAP算法的收敛速度和降低自适应权矢量计算的运算量.仿真数据和MCARM实测数据分析表明,该方法能有效抑制待检测距离单元的杂波,并能在低计算复杂度下显著提高STAP处理的收敛速度.     

二阶传输条件撕裂互连法在电大辐射中的应用

针对于大尺寸电磁辐射问题,将撕裂互连法应用于三维电大尺寸辐射问题的计算仿真。该算法是区域分解方法中的一种,求解区域划分成互不重叠的子区域,各子区域之间通过拉格朗日乘子将交界面的连续边界条件或者传输条件耦合。鉴于原来的传输条件存在不收敛或者收敛较慢情况,提出同时能在TE/TM凋落模式快速收敛的二阶传输边界条件作为子区域之间交界面的边界条件,并且引入虚拟激励流为交换信息。数值结果表明,该改进算法有效地提高了撕裂互连法在迭代求解中的收敛性。在求解三维电大辐射问题时,该算法仿真结果与有限元算法结果一致,表明撕裂互连算法是计算大尺寸电磁辐射问题的一种有效方法。     

基函数展开加速的PBSV-DDM及其在柱体散射中的应用

基于部分基础解向量的区域分解算法(PBSV-DDM)是一种新的快速高效的电磁场数值计算方法.不同于传统的区域分解算法,PBSV-DDM首先求出关于连接边界上节点的部分基础解向量,在迭代过程中,只需要对部分基础解向量做简单的线性组合就可以获得整个求解区域的最终解.然而当子区域间连接边界上的节点很多时,PBSV-DDM方法中求解基础解向量就会变得非常耗时.为此,将连接边界节点上的场值用数量较少的基函数展开,并采用欠松弛法加速部分基础解向量的迭代计算,进一步提高了PBSV-DDM的计算效率,降低了存储量.     

网络并行FDTD方法分析电大目标电磁散射

本文应用基于消息传递(Message Passing)模式的网络并行计算系统来实现并行FDTD方法.通过区域分割技术将FDTD计算区域分割成多个子域进行分别计算,各个子区域在边界处与其相邻的子区域进行切向场值的数据交换以使整个迭代进行下去,从而实现FDTD并行计算.我们采用PVM并行平台来实现并行FDTD算法.计算结果表明了本方法的正确性和有效性.     

一种自适应数据逐层分解的Reed-Solomon码迭代纠错方法及应用

该文针对Reed-Solomon码纠错算法计算复杂度较高、运算时间较长等问题,提出一种自适应数据逐层分解的Reed-Solomon码的迭代译码纠错方法。首先,接收码通过逐层分解将随机错误或突发错误分散于不同的子序列中,缩小突发或随机错误的查找范围;其次,制定约束规则确定错误数目,同时根据不同的伴随矩阵维数自适应选择迭代求解关键方程的方法,定位子序列中误码的位置;最后,计算正确码字,结束纠错。实验测试表明,该算法在保证不漏检误码的前提下,能够有效简化计算多项式的维数,减少计算量和复杂度,纠错时效优于DFT(Discrete Fourier Transform)算法和BM(Berlekamp-Massey)算法。特别是对2维码数据的纠错测试中,与传统算法相比,该算法纠错时效可提升一个数量级。     

基于节点编码的区域分解算法及其在二维散射中的应用

研究了一种高效率的基于节点编码的区域分解算法.将原始的求解区域分割为若干个相对独立的子区域,使原问题转化为若干个相对独立的子问题,通过求解公共边界上的场值,可以快速获得整个求解区域上的场值,极大地减少了存储量和计算量.此外,这种区域分解算法不仅能够快速、高效、并行地计算电大尺寸柱体的电磁散射,还特别适合于求解具有几何重复性特征的结构,如天线阵列、有限周期频率选择表面、PBG/EBG等的电磁仿真问题.数值算例验证了该方法的准确性和有效性.     

基于多层快速多极子方法的三维目标RCS高效数值求解技术

随着工程应用的不断深入,复杂三维目标雷达截面积(RCS)的高效计算越来越受关注.本文介绍了我们所发展的基于多层快速多极子方法的几种高效数值方法:后期近似迭代多层快速多极子方法、自适应射线传播多层快速多极子方法、快速远场近似多层快速多极子方法、高阶多层快速多极子方法.作为数值方法,这些方法通用性强,适于任意形状目标RCS·计算.它们不仅具有很好的计算精度,也具有优良的计算性能.对于未知量数目为N的三维电磁散射,计算量为O(NlogN)量级,存储量为O(N)量级,特别适合求解复杂三维目标RCS,有望在将来的雷达工程领域得到更深入的应用.     

基于自适应稀疏分解的探地雷达水平分层介质时延估计

传统的时延估计方法受瑞利限限制,一些基于子空间的方法可以达到高分辨或超分辨,然而,子空间方法需要处理的数据量大,计算复杂度高。提出一种新的基于自适应稀疏分解的探地雷达水平分层介质时延估计方法,自适应稀疏分解将传统的参数估计问题转化为字典学习问题。自适应稀疏分解从过完备字典中选取少量原子,其对应的时间参数即为所需估计的时延。与传统的基于子空间方法相比,该算法在低信噪比时具有更高的估计正确率,并且直接在时域进行,减少了计算复杂度。仿真及实测结果表明,该算法与MUSIC算法对比在时延估计方面具有更大的优势。     

Three-dimensional simulation of eccentric LWD tool response in boreholes through dipping formations

We simulate the response of logging-while-drilling (LWD) tools in complex thee-dimensional (3-D) borehole environments using a finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Several techniques are applied to the FDTD algorithm to improve the computational efficiency and the modeling accuracy of more arbitrary geometries/media in well-logging problems: (1) a 3-D FDTD cylindrical grid to avoid staircasing discretization errors in the transmitter, receiver, and mandrel geometries; (2) an anisotropic-medium (unsplit) perfectly matched layer (PML) absorbing boundary condition in cylindrical coordinates is applied to the FDTD algorithm, leading to more compact grids and reduced memory requirements; (3) a simple and efficient algorithm is employed to extract frequency-domain data (phase and amplitude) from early-time FDTD data; (4) permittivity scaling is applied to overcome the Courant limit of FDTD and allow faster simulations of lower frequency tool; and (5) two locally conformal FDTD (LC-FDTD) techniques are applied to better simulate the response of logging tools in eccentric boreholes. We validate the FDTD results against the numerical mode matching method for problems where the latter is applicable, and against pseudoanalytical results for eccentric borehole problems. The comparisons show very good agreement. Results from 3-D borehole problems involving eccentric tools and dipping beds simultaneously are also included to demonstrate the robustness of the method.     

Modeling of ground-penetrating-radar antennas with shields andsimulated absorbers

A three-dimensional (3-D) finite-difference time-domain (FDTD) scheme is employed to simulate ground-penetrating radars. Conducting shield walls and absorbers are used to reduce the direct coupling to the receiver. Perfectly matched layer (PML) absorbing boundary conditions are used for matching the multilayered media and simulating physical absorbers inside the FDTD computational domain. Targets are modeled by rectangular prisms of arbitrary permittivity and conductivity. The ground is modeled by homogeneous and lossless dielectric media     

An efficient and accurate technique for the incident-waveexcitations in the FDTD method

An efficient technique to improve the accuracy of the finite-difference time-domain (FDTD) solutions employing incident-wave excitations is developed. In the separate-field formulation of the FDTD method, any incident wave may be efficiently introduced to the three-dimensional (3-D) computational domain by interpolating from a one-dimensional (1-D) incident-field array (IFA), which is a 1-D FDTD grid simulating the propagation of the incident wave. By considering the FDTD computational domain as a sampled system and the interpolation operation as a decimation process, signal-processing techniques are used to identify and ameliorate the errors due to aliasing. The reduction in the error is demonstrated for various cases. This technique can be used for the excitation of the FDTD grid by any incident wave. A fast technique is used to extract the amplitude and the phase of a sampled sinusoidal signal     

On the solution of a class of large body problems with full orpartial circular symmetry by using the finite-difference time-domain(FDTD) method

This paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry. The method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem. It does so by dividing the problem into two parts: a larger 3-D region with circular symmetry, and a smaller 2-D region without circular symmetry. An finite-difference time-domain (FDTD) algorithm is used to analyze the circularly symmetric 3-D case, while a method of moments (MoM) code is employed for the nonsymmetric part of the structure. The results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system. The advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2-D as opposed to a full 3-D FDTD simulation. In addition to enhancing computational efficiency, the FDTD algorithm used in this paper also features one improvement over conventional FDTD methods: a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces. The accuracy of the method is validated via a comparison of simulated and measured results     

A hybrid Yee algorithm/scalar-wave equation approach

In this paper, two alternate formulations of the Yee algorithm, namely, the finite-difference time-domain (FDTD) vector-wave algorithm and the FDTD scalar-wave algorithm are examined and compared to determine their relative merits and computational efficiency. By using the central-difference divergence relation the conventional Yee algorithm is rewritten as a hybrid Yee/FDTD scalar-wave algorithm. It is found that this can reduce the computation time for many 3-D open geometries, in particular planar structures, by approximately two times as well as reduce the computer-memory requirements by approximately one-third. Moreover, it is demonstrated both mathematically and verified by numerical simulation of a coplanar strip transmission line that this hybrid algorithm is entirely equivalent to the Yee algorithm. In addition, an alternate but mathematically equivalent reformulation of the Enquist-Majda absorbing boundary condition based on the normal field component (relative to the absorbing boundary wall) is given to increase the efficiency of the hybrid algorithm in the modeling of open region problems. Numerical results generated by the hybrid Yee/scalar-wave algorithm for the Vivaldi antenna are given and compared with published experimental work     

求解三维问题的区域分解时域有限差分方法

该文提出一种用于三维复杂问题的区域分解时域有限差分算法(DD-FDTD)。依据待解三维复杂问题的特点,将其分解为几个子区域。每个子域中的问题相对简单,可采用适合于该区域的共形网格进行划分计算,通过插值再修正误差的办法,把各个子区域综合起来,获得原问题的解。这样,应用区域分解的思想,简化了复杂的问题。修正误差的方法,使本算法得以实现并大幅度提高了计算精度。采用本算法对三维口径天线问题进行了分析计算并与实测数据进行了比对,验证了算法的正确性。     

Modal MRTD approaches for the efficient analysis of waveguidediscontinuities

This paper, the multi-resolution time-domain (MRTD) technique is applied to the waveguide discontinuity problem for fast-scattering parameter computation. To improve the computational efficiency, both three-dimensional (3-D) waveguide regions, including discontinuities, and one dimensional (1-D) homogeneous waveguide region, terminated with the modal absorbing boundary condition (ABC), are simulated in the wavelet domain with the mode composition/expansion algorithm from the modal analysis. A WG-90 rectangular waveguide with a thick asymmetric iris is analyzed and the numerical results are compared with conventional finite-difference time-domain (FDTD) results and mode-matching results     

Conservative and Provably Stable FDTD Subgridding

The finite difference time domain (FDTD) method is a common, robust simulation technique for transient electromagnetic interactions with complicated structures. However, the standard FDTD method is limited to cartesian grids everywhere in the computational grid. Many practitioners have extended FDTD to handle multiresolution problems by using finer grids near structures with small geometrical features abutted to coarse grids in regions of empty space. Unfortunately, subgridding implementations based on interpolation or extrapolation of neighboring field values can exhibit late time instabilities. Herein, a subgridding method based on multigrid finite element principles will be developed and its stability proven. Numerical results will assess its performance in 2-D and 3-D.     

A new 2-D FDTD method applied to scattering by infinite objects with oblique incidence

A new two-dimensional (2-D) finite-difference time domain (FDTD) method applied to scattering by infinite objects with oblique incidence is proposed. 2-D Maxwell's equations, differential equations, and perfectly matched layer (PML) absorbing boundary conditions (ABC) are derived. The incident wave, computed by the 1-D FDTD method, is set on the connecting boundary. The accuracy and the efficiency of the proposed method have been verified by comparing the results of the split-field periodic FDTD method, the sine-cosine method, and the transmission line theory method with the proposed method.     

3-D ADI-FDTD method-unconditionally stable time-domain algorithmfor solving full vector Maxwell's equations

We previously introduced the alternating direction implicit finite-difference time domain (ADI-FDTD) method for a two-dimensional TE wave. We analytically and numerically verified that the algorithm of the method is unconditionally stable and free from the Courant-Friedrich-Levy condition restraint. In this paper, we extend this approach to a full three-dimensional (3-D) wave. Numerical formulations of the 3-D ADI-FDTD method are presented and simulation results are compared to those using the conventional 3-D finite-difference time-domain (FDTD) method. We numerically verify that the 3-D ADI-FDTD method is also unconditionally stable and it is more efficient than the conventional 3-D FDTD method in terms of the central processing unit time if the size of the local minimum cell in the computational domain is much smaller than the other cells and the wavelength