论文（未排版）

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摘 要

为了适应日益增长的宽带信号和非线性系统的工程应用，用于分析瞬态电磁散射问题的时域积分方程方法研究日趋活跃。本文以时域积分方程时间步进算法及其快速算法为研究课题，重点研究了时间步进算法的数值实现技术、后时稳定性问题以及两层平面波算法加速计算等，主要研究内容分为四部分。 ??

关键词：时域电磁散射，时域积分方程，时间步进算法，后时不稳定性，时域平面波算法

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ABSTRACT

With the widespread engineering applications ranging from broadband signals and non-linear systems, time-domain integral equations (TDIE) methods for analyzing transient electromagnetic scattering problems are becoming widely used nowadays. TDIE-based marching-on-in-time (MOT) scheme and its fast algorithm are researched in this dissertation, including the numerical techniques of MOT scheme, late-time stability of MOT scheme, and two-level PWTD-enhanced MOT scheme. The contents are divided into four parts shown as follows.

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Keywords: time-domain electromagnetic scattering, time-domain integral equation

(TDIE), marching-on in-time (MOT) scheme, late-time instability, plane wave time-domain (PWTD) algorithm

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目录

摘 要 ............................................................................................................................... I ABSTRACT .................................................................................................................... II 第一章 绪 论 .................................................................................................................. 5 1.1 研究工作的背景与意义 ........................................................................................... 5 1.2 时域积分方程方法的国内外研究历史与现状 ....................................................... 5 1.3 本文的主要贡献与创新 ........................................................................................... 5 1.4 本论文的结构安排 ................................................................................................... 5 第二章 时域积分方程基础 ............................................................................................ 6 2.1 时域积分方程的类型 ............................................................................................... 6 2.2 空间基函数与时间基函数 ....................................................................................... 6

2.2.1 空间基函数 ................................................................................................................... 6 2.2.2 时间基函数 ................................................................................................................... 7

2.3 入射波 ....................................................................................................................... 7 2.6 本章小结 ................................................................................................................... 8 第三章 时域积分方程数值方法研究 ............................................................................ 9 3.1 时域积分方程时间步进算法的阻抗元素精确计算 ............................................... 9 3.2 时域积分方程时间步进算法阻抗矩阵的存储 ....................................................... 9

3.2.1 时域积分方程时间步进算法产生的阻抗矩阵的特征 ............................................... 9 3.2.2 数值算例与分析 ........................................................................................................... 9

3.3 时域积分方程时间步进算法矩阵方程的求解 ..................................................... 10 3.4 本章小结 ................................................................................................................. 11 第四章 全文总结与展望 .............................................................................................. 12 4.1 全文总结 ................................................................................................................. 12 ?? ................................................................................................................................ 12 4.2 后续工作展望 ......................................................................................................... 12 致 谢 ............................................................................................................................ 13

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