三维电大目标散射求解的多层快速多极子方法

为进一步提高对电大尺寸目标散射求解的能力,详细研究了多层快速多极子方法.重点设计了用于多层快速多极子方法的各种优化方法包括Morton编号、转移因子修正内插技术与外向波重复存储策略.对于未知量数目为N的三维电磁散射,数值实验显示多层快速多极子方法具有O(NlogN)量级的计算量、O(N)量级的存储量,特别适合求解三维电大尺寸目标的电磁散射.利用该方法在单机(内存1Gb)上成功计算了未知量为25万的电大尺寸目标散射.     

三维导电目标电磁散射的高阶多层快速多极子方法

为进一步提高电大尺寸目标散射求解能力,采用了基于多层快速多极子方法的高阶方法.与低阶相比,该方法所需未知量数目大大减少,而计算精度不变,因而具有比传统多层快速多极子方法更高的计算效率.给出的典型计算结果充分说明了高阶多层快速多极子方法的高效性.     

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.     

一种电大尺寸组合体散射的快速计算方法

采用自适应多层快速多极子算法分析电大尺寸组合体的雷达散射截面。推导了组合体表面的积分方程,通过将基函数和权函数分别用不同空间位置上的点源函数展开,自适应多层快速多极子算法实现了阻抗积分的快速计算,通过采用射线传播法,远场近似和对称性计算法则使转移因子的计算效率大大提高,所有转移过程可由快速傅里叶变换计算完成。这种算法计算组合体散射时所需的计算时间和内存显著降低,且数值计算结果和实际测试结果吻合良好。     

FMM用于快速计算电大腔体的RCS

利用迭代物理光学法(IPO)计算一般电大尺寸腔体的电磁散射特性,在迭代过程中用快速多极子方法(FMM)加速计算.在雅可比最小残差法(JMRES)的积分运算中引入FMM并与共扼梯度法(CG)的计算效率进行了比较.采用结构化分组,利用转移因子的平移不变性对计算和存储进行了优化.计算结果表明这些加速方法是有效的并能极大地提高计算效率.     

一种自适应的射线传播多层快速多极子方法

在多层快速多极子方法中,外向波向内向波的转移计算是主要的计算量.传统的转移过程需要计算众多的角谱分量,造成较多计算时间和内存的耗费.一种自适应射线传播多层快速多极子方法可用以降低转移过程计算量.数值计算结果表明,这种算法能够保持合理精度的同时大大减少计算量,适于三维电大尺寸目标RCS的快速求解.     

并行多层快速多极子的高效预条件技术

多层快速多极子法是基于矩量法的快速算法,具有较低的计算复杂度和存储复杂度,被广泛应用于目标电磁散射特性分析。对于复杂结构电磁目标,由于矩阵条件数较差,往往存在迭代收敛慢甚至不收敛的问题。针对这一情况,文中利用快速多极子的近区矩阵,结合稀疏矩阵方程求解构造了一种高效预条件。数值实例表明该方法相比于块对角预条件效果更好,能有效加速多层快速多极子迭代过程。     

IPO结合FMM，RPFMM，FaFFA方法快速计算电大腔体的RCS

迭代物理光学法结合快速多极子(IPO+FMM)方法,可以快速计算电大腔体的电磁散射特性。传统的快速多极子(FMM)方法需要计算两组的转移因子以及转移过程的全部角谱分量,计算开销是非常大的。随着组间距离的增大,转移过程可以用射线多极子(RPFMM)简化计算,为了充分利用射线多极子方法中参与计算的有效角谱分量随着组间距离增大而变少的特性,采用一种随着组间距离增大自适应调整参与计算的角谱分量的锥形区域的射线多极子方法(RPFMM),当两组距离足够大而位于远场时,用远场近似方法(FaFFA)进一步简化计算。结果表明该方法能在保持计算精度的同时并能较IPO+FMM方法进一步减少计算资源占用、提高计算速度。     

邻居预条件加速的多层快速非均匀平面波算法

采用邻居预条件加速的多层快速非均匀平面波算法求解三维导电目标的电磁散射.通过分组,将耦合划分为附近和非附近区,对于非附近区采用索末菲恒等式对格林函数展开,用修正最陡下降路径代替索末菲积分路径进行数值积分.采用内插与外推技术将复角谱序列转换成均匀实角谱序列,以便于算法的高效实施.该算法的计算复杂度与多层快速多极子相当,且更具潜在优势.为改善迭代特性,本文研究了一种邻居预条件方法,加速迭代收敛,数值结果验证了算法的准确和高效.     

电大均匀介质目标三维散射的并行多层快速多极子计算

实现了计算电大均匀介质体散射问题的高效混合并行混合场积分方程(Electric and Magnetic Current Combined-Field Integral Equation, JMCFIE)求解, 在单纯消息传递接口(Message Passing Interface, MPI)并行基础上采用共享存储并行编程(Open Multi-Processing, OpenMP)进一步提升性能.该混合MPI与OpenMP的并行多层快速多极子技术通过灵活的进程和线程策略, 提升了负载平衡和可扩展性.数值实验展示了此混合MPI与OpenMP的并行多层快速多极子技术的计算能力, 计算了不同尺寸的电大目标体(包含一个半径120 m、1.1亿未知数目的介质球).     

A FAFFA-MLFMA algorithm for electromagnetic scattering

Based on the multilevel fast multipole algorithm (MLFMA), an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation, where the fast far-field approximation (FAFFA) is combined with MLFMA. The translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many k/spl circ/ directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single k/spl circ/ direction is involved in the translator. The condition for using FAFFA and the way to efficiently incorporate FAFFA with MLFMA are discussed. Complexity analysis illustrates that the computational cost in FAFFA-MLFMA can be asymptotically cut by half compared to the conventional MLFMA. Numerical results are given to verify the efficiency of the algorithm.     

Broadband Müller-MLFMA for Electromagnetic Scattering by Dielectric Objects

The multilevel fast multipole algorithm (MLFMA) is very efficient for solving large-scale electromagnetic scattering problems. However, at low frequencies, or when the discretization is small compared with the wavelength, both the MLFMA and the underlying integral equation formulation typically suffer from a subwavelength breakdown. For the electromagnetic scattering from a homogeneous dielectric object, we obtain a stable and well-conditioned surface integral formulation using a variant of the classical Muumlller formulation and linear basis functions. To overcome the subwavelength breakdown of the MLFMA, we use both propagating and evanescent plane waves to represent the fields. The implementation is based on a combination of the spectral representation of the Green's function and Rokhlin's translation formula. We also present a new interpolation scheme for the evanescent part, which significantly improves the error-controllability of the MLFMA-implementation. Several numerical results verify both the error-controllability and scalability of the proposed algorithm     

An Efficient Implementation of the Combined Wideband MLFMA/LF-FIPWA

An efficient implementation of the low frequency fast inhomogeneous plane wave algorithm (LF-FIPWA) combined with the multilevel fast multipole algorithm (MLFMA) is presented. The seamless combination of the LF-FIPWA with the MLFMA renders a powerful method applicable for a wide frequency range. As the MLFMA is already well established we will describe possibilities for an efficient formulation of the LF-FIPWA: An implicit filtering reduces the bandwidth of the integrand. An interpolation of the excitation vectors is introduced which avoids dealing with the in general complex angles. An adaptive quadrature rule on the path in the complex plane further increases the efficiency. We present a simple but accurate interpolation and anterpolation method on this path. In addition, for symmetric objects or for perfectly conducting ground the incorporation of a symmetry wall is described.      

Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling k/spl circ/ directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling k/spl circ/ directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single k/spl circ/ is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.     

An IE-ODDM-MLFMA Scheme With DILU Preconditioner for Analysis of Electromagnetic Scattering From Large Complex Objects

For electrically large complex electromagnetic (EM) scattering problems, huge memory is often required for most EM solvers, which is too difficult to be handled by a personal computer (PC) even a workstation. Although the multilevel fast multipole algorithm (MLFMA) effectively deals with electrically large problems to some extent, it is still time and memory consuming for very large objects. In order to further reduce the CPU time and the memory requirement, a hybrid algorithm, based on the overlapped domain decomposition method for integral equations (IE-ODDM), MLFMA and block-diagonal, incomplete lower and upper triangular matrices (DILU) preconditioner, is proposed for the analysis of electrically large problems. The dominant memory requirement for plane wave expansions in the three processes of aggregation, translation and disaggregation in the MLFMA is drastically reduced by the first two techniques. The iterative procedure for each overlapped subdomain solved by the MLFMA is effectively sped up by the DILU preconditioner. After integrating these techniques, the proposed hybrid algorithm is more efficient in computing time and memory requirement compared to the conventional MLFMA and is more suitable for analyzing very large EM scattering problems. Enough accurate solution can be obtained within quite a few outer iterations, where an outer iteration means a complete sweep for all the subdomains. Some numerical examples are presented to demonstrate its validity and efficiency.     

Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid Integral equations in electromagnetics

In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.     

Block storing method for efficient storage of near group impedance in MLMFA

The block storing method (BSM) based on Morton Key ordering for the efficient storage of the near group interaction matrix in the multilevel fast multipole algorithm (MLFMA) is presented. The proposed method is applied in a parallel MLFMA and a scattering problem with nearly 5 300 000 unknowns is solved, for which the BSM saves 6.84 GB without any extra cost.     

用于复杂目标三维矢量散射分析的快速多极子方法

本文着重介绍了一种用于复杂目标三维电磁散射精确建模和数值分析的高型高效数值方法,即快速多极子方法和多层快速多极子方法。     

基于混合离散方式的等效原理算法精度改进

针对等效原理算法（equivalent principle algorithm，EPA）中的单位算子采用传统数值离散方式导致精度差的问题，提出了一种混合的数值离散方式来提高计算精度.该混合离散方式将等效面上的电流用传统RWG（Rao-Wilton-Glisson）基函数展开，磁流用BC（Buffa-Christiansen）基函数展开，再分别用$ {\boldsymbol{\hat n}}$×BC和$ {\boldsymbol{\hat n}}$×RWG作为测试函数对电流和磁流进行测试，即在单位算子的对偶空间里对其进行测试.本文还将多层快速多极子方法（multilevel fast multipole algorithm，MLFMA）用于加速EPA中的矩矢相乘计算.最后通过数值算例说明了该方法的正确性和有效性.