稳定的欠定方程快速算法及其在复杂精细目标电磁散射精确建模中的应用

The precise modeling and fast analysis of electromagnetic scattering from complex and fine targets have important significance in the field of electromagnetic system design, which involved in new generation information technology. This project focuses on the efficient solution of large-scale linear systems, based on compressive sensing(CS),a stable and fast algorithm for underdetermined equation is proposed in MOM, which is implanted in Calderón Multiplicative Preconditioner(CMP) for analyzing electromagnetic scattering of complex fine target, thus the simulation result can be fast obtained with the high accuracy. The main research work can be summarized as follows.(1) For constructing CMP efficient computing model, the proposed fast algorithm will be applied to solve multiple nested linear systems in CMP technology, and from which the prior knowledge can be extracted;(2)The CS key techniques will be investigated and optimized to complete the revision of the computing model step by step ,such that the computing model can be extended to three dimensional targets while further improving the computational efficiency;(3) For complex fine target of non-uniform subdivision，the revised computing model in conjugation with the new excitation source and advanced frequency-sweep analysis method will form novel schemes，respectively，which can efficiently analyze scattering characteristics of complex and fine targets in both spatial and frequency domains.Given generality of the proposed computing models, research achievement can also pave a novel way to solve efficiently similar linear system.

针对复杂精细目标的电磁散射精确建模及快速计算，在新一代信息技术所涉及的电磁系统设计领域中具有重要的意义。本申请以高效求解大规模线性系统为主线，在矩量法框架下，基于压缩感知(CS)理论提出稳定的欠定方程快速算法，考虑将其贯穿于Calderón乘式预条件(CMP)在复杂精细目标电磁散射分析中的应用体系，旨在保证高精度的前提下，提升计算速度。具体研究工作概括如下：(1)利用所提快速算法对CMP技术中多个嵌套线性系统进行求解，从中提取先验知识，构建CMP高效计算模型；(2)通过对CS关键技术的研究，逐步完成计算模型的优化工作，在将该模型适用范围扩展至三维目标的同时，进一步提升计算效率；(3)针对非均匀剖分的复杂精细目标，将修正后的计算模型分别与新型激励源及先进的宽频方法相结合，形成高效分析电磁散射频空特性的新方法。鉴于计算模型的通用性，研究成果亦可为高效处理类似线性系统提供新的解决途径。

项目组聚焦复杂精细结构电磁散射特性的高效分析问题，经过三年的实施周期，较好的完成了既定研究目标，具体研究内容概括如下：首先，基于压缩感知理论提出稳定的欠定方程快速算法，并将其引入CMP 技术中，搭建了Calderón 乘式预条件高效计算模型；其次，开展了所提模型在精细结构电磁散射中的应用研究，通过对观测矩阵、稀疏变换、恢复算法三要素的优化，将其植入到各种应用场景的类线性系统中；最后，在此基础上，将所提模型分别与宽角度新型激励源及先进宽频技术相结合，构建了复杂精细结构电磁散射频空特性高效分析方法。此外，鉴于所提算法的通用性，探索了其在微波器件设计等领域中的应用。