电磁散射分析的新型预条件及快速求解技术

In practical engineering, the electromagnetic scattering of complex targets and electromagnetic radiation features on the large platform are urgently required to be efficiently analyzed. To analyze electrically large structures, the iterative solvers usually have to be adopted. However the iterative solvers may converge slowly for complex structures, and are less efficient for multiple right-hand side (RHS) vectors. It is very time-consuming even if computing with modern high-performance workstation and servers. To address these challenges, we propose to study geometric multigrid iterative method to accelerate the analysis of surface integral euqaitons with Rao-Wilton-Glisson basis functions, and take a series of measures to enhance the efficiency. Spectral preconditioner for multi-resolution basis function is also proposed and a fast construction scheme of the preconditioner is studied. We plan to launch a deeply investigation of a novel solving scheme called model order reduction based on Krylov subspace technique. In the technique, a sequence of orthonormal vectors are produced by implementing an Arnoldi process and are utilized to span the unknown vectors. After performing a Galerkin procedure, we achieve a system with much smaller order than the original one using ordinary subdomain basis function. The model order reduction is a promising technique for fast solving multiple RHS vectors. We propose to study a variety of techniques, including preconditioning schemes, deflated and augmented Krylov subspace schemes and block Krylov subspace schemes and so on, to improve the efficiency of model order reduction scheme. Parallelization software equiped with the proposed technique will be developed and optimized to analyze the scattering and radiation from the electrically large and complex structures.

在目标探测、目标识别等工程应用领域，迫切需要高精度地分析目标电磁散射特性和复杂平台上的电磁辐射特性。采用积分方程快速算法分析目标电磁特性时，对电大尺寸复杂结构经常出现迭代解法难以收敛的情况，分析效率亟待提高。针对这一问题，项目将在现有多层快速多极子等快速分析算法基础上，研究一系列提高电磁场积分方程分析效率的方法，研究基于 Rao-Wilton-Glisson (RWG) 基函数的几何多重网格迭代算法的实现与改进方法，研究基于多分辨基函数的特征谱预条件技术及其快速构造方法；针对求解单站雷达散射特性时迭代解法效率不高的问题，研究基于 Arnoldi 过程的模型降阶技术分析多右边向量问题，研究采用预条件、收缩和扩张 Krylov 子空间、块 Krylov 子空间等多种技术来优化模型降阶技术，并研究将模型降阶技术用于分析多参数扫描的电磁问题。最后还将开发出基于高性能并行计算平台的电磁分析软件。

针对目标探测、识别及考虑复杂平台背景下的高精度电磁散射/辐射特性分析，开展在现有多层快速多极子等快速分析算法基础上，研究一系列提高电磁场积分方程分析效率的方法；研究基于Rao-Wilton-Glisson (RWG) 基函数的几何多重网格迭代算法的实现与改进方法；研究基于多分辨基函数的特征谱预条件技术及其快速构造方法。改善收敛速度，提高分析效率。针对求解单站雷达散射特性时迭代解法效率不高的问题，研究基于Arnoldi过程的模型降阶技术分析多右边向量问题，研究采用预条件、收缩和扩张Krylov子空间、块Krylov子空间等多种技术来优化模型降阶技术，并研究将模型降阶技术用于分析多参数扫描的电磁问题。利用提出的算法开发出基于高性能并行计算平台的电磁软件。

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