【作者】 晏璎；

【导师】 梁昌洪；

【作者基本信息】 西安电子科技大学 ， 电磁场与微波技术， 2013， 博士

【摘要】 近年来，并行电磁算法以其优越的加速性能受到了人们的广泛关注，越来越多地被应用于大规模电磁问题的求解和仿真中。论文以时、频域电磁算法的“并行应用”为主线，以基于ScaLAPACK和MPI数学库的并行高阶矩量法，并行物理光学方法，并行高阶矩量法、物理光学法的混合方法，以及并行时域积分方程混合自适应交叉近似法(Adaptive CrossApproximation或ACA)为研究对象，计算了金属、介质目标的时、频域电磁辐射、散射响应。论文所取得的主要研究成果为：1.采用高阶基函数替代传统的低阶基函数（如RWG基函数）展开模型的电磁流未知量，从而解决了低阶矩量法在处理电大尺寸模型时，由于10的网格剖分尺寸所带来的未知量数目巨大，消耗计算机内存多，硬件资源不足等问题；采用Poggio-Miller-Chang-Harrington-Wu (PMCHW)积分方程分析金属、介质混合体目标；为了加快问题的求解速度，提高效率，结合MPI和ScaLAPACK数学库自身的性能特点提出了一种高效的阻抗矩阵并行填充策略，该并行策略可以保证算法具有良好的并行效率和负载均衡性；2.利用并行高阶矩量法解决了一大批电磁问题仿真，合理的求解时间和高精度的计算结果说明该算法可用于解决实际工程问题；3.针对金属、介质混合体目标，从阻抗边界条件出发，应用传输线理论，研究了一种基于三角形面片建模，以路德维格(Ludwig)积分方法求解积分表达式的新的物理光学方法。同时，为了加速计算，结合MPI数学库研究了算法的高效率并行方案。该算法可处理阻抗表面模型，纯介质体，多层介质涂覆目标以及传统的理想导电体(Perfect Electric Conducting或PEC)模型，用于预估自由空间中、半空间中电大尺寸模型的单、双站雷达散射截面(Radar Cross Section或RCS)；研究了并行高阶矩量法、物理光学混合方法用以分析机载复杂天线的受扰辐射方向图；提出了一种崭新的“迭代矢量场”方法，该方法仅需要极少的迭代次数就可以获得稳定的解；4.研究了基于阶数步进(Marching-on in Degree或MOD)的并行时域积分方程方法(TDIE)。通过引入拉盖尔多项式(Laguerre polynomials)来展开时域积分方程中的暂态物理量，从而解决了传统时间步进(Marching-on in Time或MOT)方法中时间轴后半段解不稳定的问题；将自适应交叉近似方法(Adaptive CrossApproximation或ACA)应用到时域积分方程的阻抗矩阵填充中，有效地降低了计算过程中的内存资源需求，且计算精度不会受到太大的影响；为了提高计算效率，基于MPI和ScaLAPACK数学库，研究了TDIE-ACA算法的阻抗矩阵并行填充和矩阵方程并行求解的高效策略。更多还原

【Abstract】 In recent years, more and more attention has been paid to the parallelelectromagnetic (EM) numerical methods due to their good acceleration performance.As “parallel” to be the clue, this dissertation studies the parallel algorithms based onMPI and ScaLAPACK, including parallel Higher-order Method of Moments, parallelPhysical Optics, parallel hybrid method of Higher-order Method of Moments andPhysical Optics, and parallel hybrid method of Time-domain Integral Equation andAdaptive Cross Approximation, to analyze the scattering and radiation problems ofmetal and dielectric model. This dissertation’s major contributions are outlined asfollows:1. Higher-order basis is used to expand the unknowns so as to reduce the number ofunknowns and the memory required compared to those of RWG basis; usingPoggio-Miller-Chang-Harrington-Wu (PMCHW) integral equation to solve the EMproblem of metal and dielectric model; proposing a parallel matrix filling scheme toobtain a good load balancing and parallel efficiency;2. Using parallel Higher-order MoM to solve a lot of challenging EM problems.The high accuracy and good computational performance demonstrate that this methodcan be used to effectively solve the practical engineering problem;3. Based on impedance boundary condition and transmission line theory, thisdissertation studies a new Physical Optics (PO) method, which employs the triangularpatch modeling technique and uses Ludwig method to calculate the integral; moreover,this dissertation studies the parallelization of PO based on MPI and ScaLAPACK, whichcan be used to analyze the monostatic and bistatic RCS of the metal, impedance anddielectric model placed in free-space or half space; in addition, this dissertation alsostudies the parallel hybrid method of Higher-order MoM and PO, which uses a newhybrid scheme named “iterating vector fields technique”. This method can obtain astable solution with only a few iterations;4. This dissertation studies the parallel Time-domain Integral Equation (TDIE)based on Marching-on in Degree (MOD) solver. The introduction of Laguerrepolynomial can avoid the problem of obtaining an unstable solution in late-time regionwhich exists in Marching-on in Time (MOT) solver; to reduce the memory required inthe matrix filling, this dissertation combines the Adaptive Cross Approximation (ACA)with TDIE; Finally, parallel technique based on MPI and ScaLAPACK is applied in this hybrid method to improve the computational efficiency.更多还原