多极子与区域分解型高效电磁计算算法及其应用

发布时间：2018-05-10 04:51

本文选题：电磁散射 + 表面积分方程法　；参考：《北京理工大学》2014年博士论文

【摘要】：本文以解决实际电磁工程应用中典型问题，譬如电大深腔、电大介质体、涂敷体的计算分析为目的，利用多极子与区域分解快速算法，对均匀介质面积分方程矩量法、有限元方法、以及混合有限元、边界元和多层快速多极子方法（简称合元极方法）三种方法的快速算法进行了设计、实现、及其数值性能研究，以提高电磁仿真的计算能力。与此同时，将实现的快速算法应用于分析目标特性、光镊技术等，解决了一系列工程应用中的实际难题。在快速算法研究方面，本文主要研究了计算电磁学中的均匀介质面积分方程多层快速多极子算法，有限元区域分解快速算法，区域分解高阶合元极算法。对于均匀介质面积分方程多层快速多极子算法，主要研究了电磁联合场积分方程（the electric andmagnetic current combined-field integral equation，JMCFIE）结合并行多层快速多极子算法求解均匀介质体电磁问题。对于有限元区域分解快速算法，主要研究了有限元区域分解算法中最强有力的算法之一的撕裂对接法（finite element tearing andinterconnecting Method, FETI）。对于区域分解高阶合元极算法，首先设计了用于求解电大深腔散射问题的按层消去算法，其次设计了针对采用高阶叠层基函数的合元极h-p-MUS预处理算法。最后，将有限元区域分解算法与合元极算法结合起来，提出并实现了区域分解合元极算法以及基于区域分解的合元极预处理技术，极大的提高了合元极算法的计算能力。同时，为了提高算法的计算能力与实际应用性，结合了基于分布式消息传递方式的MPI以及基于共享内存的OpenMP并行化实现。在快速算法应用方面，本文计算了一系列极具挑战性的实际问题。利用并行均匀介质面积分方程多层快速多极子算法，快速精确计算了直径达240波长，，未知数过亿的电大均匀介质体目标散射问题。同时，将算法引入到具有重大实际应用价值的光学操控-光镊技术的仿真计算中来，实现了对任意形状均匀目标粒子在有形波束中辐射压力与辐射扭矩的计算，以及对任意形状软体粒子的表面张力的仿真分析。利用区域分解合元极算法解决了过亿未知数模拟的大型微带天线阵列的计算；利用并行高阶合元极算法计算了尺寸为4040100的电大深腔以及复杂的带有发动机叶片结构的飞机进气道模型；最终利用并行区域分解高阶合元极算法计算分析了电大尺寸非均匀结构或周期性结构，如电大涂敷结构，复合结构，周期性阵列结构如天线阵、频率选择表面等的散射特性。
[Abstract]:In order to solve the typical problems in practical electromagnetic engineering application, such as the calculation and analysis of electrically large deep cavity, electrically large dielectric body and coating body, this paper applies the fast algorithm of multipole and domain decomposition to the moment method of the uniform medium area partial equation. The fast algorithms of finite element method, mixed finite element method, boundary element method and multilayer fast multipole method are designed, implemented, and their numerical properties are studied to improve the computational power of electromagnetic simulation. At the same time, the fast algorithm is applied to analyze the target characteristics, optical tweezers technology and so on, which solves a series of practical problems in engineering applications. In the aspect of fast algorithm, this paper mainly studies the multilayer fast multipole algorithm, the finite element domain decomposition fast algorithm, the domain decomposition high order combining pole algorithm. For the multilayer fast multipole algorithm of uniform dielectric area subequation, the electromagnetic field integral equation and the electric andmagnetic current combined-field integral equation- JMCFIEs are studied to solve the electromagnetic problem of homogeneous dielectric volume with parallel multilayer fast multipole algorithm. For the fast algorithm of finite element domain decomposition, finite element tearing andinterconnecting method (FETI), one of the most powerful algorithms of finite element domain decomposition, is studied in this paper. For the domain decomposition high-order combinatorial pole algorithm, firstly, a layer-elimination algorithm is designed to solve the scattering problem of electrically large deep cavity, and then a h-p-MUS preprocessing algorithm based on the higher-order laminated basis function is designed to solve the problem of electrically large cavity scattering. Finally, combining the finite element domain decomposition algorithm and the combining pole algorithm, the paper proposes and implements the domain decomposition combining pole algorithm and the preprocessing technology based on domain decomposition, which greatly improves the computing ability of the combined pole algorithm. At the same time, in order to improve the computing power and practical application of the algorithm, the MPI based on distributed messaging and the parallel implementation of OpenMP based on shared memory are combined. In the application of fast algorithm, this paper calculates a series of challenging practical problems. By using the multilayer fast multipole algorithm of parallel homogeneous dielectric area equations, the scattering problem of electrically large homogeneous dielectric bodies with a diameter of 240 wavelength and over 100 million is calculated quickly and accurately. At the same time, the algorithm is introduced into the simulation calculation of optical manipulation-optical tweezers technology, which has great practical application value, and the radiation pressure and radiation torque of arbitrary uniform target particles in visible beam are calculated. And the simulation analysis of surface tension of soft particles with arbitrary shape. The computation of large microstrip antenna array simulated by unknowns is solved by using the domain decomposition combining pole algorithm. The parallel high-order joint pole algorithm is used to calculate the large electrically large cavity with size of 4040100 and the complex aircraft intake port model with engine blade structure. Finally, the scattering characteristics of electrically large non-uniform or periodic structures, such as electrically large coated structures, composite structures, periodic array structures such as antenna arrays and frequency-selective surfaces, are calculated and analyzed by using parallel domain decomposition high-order combining pole algorithm.
【学位授予单位】：北京理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM15

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