MS004305-电磁场边值问题数值分析（在线课程）

研究生课程开设申请表

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 课院（系、所）： 信息科学与工程学院

 课程申请开设类型： 新开□     重开□     更名□（请在□内打勾，下同）

一、课程介绍（含教学目标、教学要求等）（300字以内）

本课程将介绍求解电磁场问题的多种数值方法，包括差分方法，积分方程方法，有限元方法以多种及快速算法等等，目的是让研究生了解并掌握电磁场问题的主要的现代数值分析方法，从而为开展与计算电磁学有关的研究打下坚实的基础。

教学要求：要求学生通过课堂学习，掌握各种方法的基本原理及其应用，通过课后阅读教材和有关参考文献了解各种方法的更深入的内容和国内外的最新研究进展。

二、教学大纲（含章节目录）：（可附页）

第一章 电磁场理论基础

§1.1  Maxwell方程组

§1.2  边界条件

§1.3  位函数

§1.4  问题描述－导波问题、散射问题、辐射问题

第二章 直线法

§2.1 直线法原理

§2.2 直线法在导波问题和散射问题上的应用

第三章 传输线矩阵法

§3.1 传输线矩阵法原理

§3.2 传输线矩阵法的应用

第四章 模式匹配法

§4.1模式匹配法原理

§4.2模式匹配法的应用

第五章 电磁场微分方程的数值方法－有限差分法

§5.1  静场方程（Laplace方程）的有限差分方法

§5.2  波动方程有限差分法

§5.3  扩散方程的有限差分方法

第六章^*线性代数方程组的迭代解法

§6.1  迭代方法描述

§6.2 Jacobi 迭代法；Gauss-Seidel 迭代法；超松驰迭代法（SOR（Successive Over-Relaxation）；对称超松驰法（SSOR迭代法）

第七章  时域有限差分法

§7.1 问题描述

§7.2  Yee网格下的差分方程

§7.3 边界条件

§7.4 应用算例

第八章 频域有限差分法

§8.1 问题描述

§8.2  Yee网格下的差分方程

§8.3 边界条件

§8.4 应用算例

第九章 有限元方法

§9.1  二维静场的变分问题描述

§9.2  区域剖分和插值函数（二维问题）

§9.3  Ritz方法和Galerkin方法

§9.4  单元矩阵与整体系数矩阵

§9.5  应用算例

第十章 对称正定矩阵解法-共轭梯度法（Conjugate Gradient Method）

§10.1  问题描述

§10.2  共轭梯度法

§10.3  预条件共轭梯度法

§10.4  复矩阵和对称不定矩阵的共轭梯度法

第十一章 矩量法与电磁场问题的变分原理

§11.1  变分问题描述

§11.2  电磁场问题的变分形式

§11.3  矩量法基本原理

§11.4  基函数和权函数的选取

§11.5  矩量法应用

第十二章 区域分解法  

§12.1  概念描述

§12.2  Schwarz交替法

§12.3  D－N交替法

§12.4  Helmoholtz 方程的区域分解法

§12.5  Maxwell 方程的区域分解法

§12.6  应用算例

第十三章 矢量有限元方法

§13.1  问题描述

§13.2  三角剖分单元的基函数

§13.3  单元矩阵计算

§13.4  场的连续性与系数矩阵

第十四章^*二维电磁问题的（积分方程）边界元方法

§14.1  边界元方法基本原理

§14.2  数值积分和数值解法

§14.3  边界元方法应用

第十五章^*譜域法

§15.1  譜域法基本原理

§15.2  譜域法应用

第十六章^*不变性测试方程法

§16.1  不变性测试方程法（MEI方法）基本原理

§16.2  MEI系数的确定和测试子

§16.3  MEI方法应用

第十七章 积分方程法

§17.1 Maxwell方程积分形式

§17.2 电磁场边值问题

§17.3 电磁场积分方程

§17.4 应用算例

第十八章 积分方程的重叠型区域分解算法

§18.1区域分解方法背景和历史

§18.2积分方程的重叠型区域分解算法

§18.3缓冲区的大小和确定

§18.4计算复杂度分析

§18.5介质积分方程的重叠型区域分解算法

§18.6 应用算例

第十九章 多层快速多极子的重叠型区域分解算法

§19.1 多层快速多极子和预条件器

§19.2 多层快速多极子的重叠型区域分解算法

§19.3 算法特征、计算复杂度分析

§19.4 基于RWG和底层盒子的重叠型区域分解算法

§19.5 应用算例

第二十章 矩阵插值的快速算法

§20.1 矩阵元素关于频率的表达式

§20.2 几类矩阵插值算法

§20.3 频带内样点优化

§20.4 应用算例

注：带星号章节为选讲内容。

三、教学周历

四、主讲教师简介：

洪伟：1982年毕业于解放军信息工程学院，1985和1988年分别于东南大学获硕士、博士学位。现为东南大学无线电工程系教授、博士生导师、教育部长江学者计划特聘教授。

主要学术方向：计算电磁学、微波毫米波理论与技术、无线通信中的射频技术。近年来，承担国家自然科学基金项目（国家杰出青年基金项目等）、“863”重大项目、国家科委和教委基金项目等四十多个项目的研究任务。在国内外学术刊物（如IEEE Trans. on MTT、AP、EMC、MWCL、MGWL、IEE Pt.H、Electron. Lett.、Radio Science、AEU、“中国科学”等）和会议上发表论文200多篇，出版专著2部，参写国际国内著作4部。曾获国家自然科学四等奖一项（第三获奖人）、国家教委科技进步一等奖两项（第一、第二获奖人）、二等奖一项（第七获奖人）、江苏省科技进步二等奖、三等奖各一项（第一、第二获奖人）。曾赴美国加州伯克利大学、加州Santa Cruz 大学、纽约州立大学、加州Ultima公司、日本通信综合研究所、香港中文大学等访问研究和讲学。

孙连友：1990年7月毕业于复旦大学数学研究所，获硕士学位。2003年7月于东南大学无线电工程系获博士学位。1990年到1998年1月期间在东南大学数学系工作，从事教学和应用数学方面的研究。2005年8月至2006年8月由国家留学基金委公派到加拿大McGill大学从事博士后研究。目前，主要从事微波毫米波理论与技术、计算电磁学数值理论和计算方法方面的教学和科研工作。在IEEE和国内核心期刊及国际会议上发表论文十余篇。并合著有《电磁场边值问题的区域分解算法》，由科学出版社出版。

李卫东：2007年毕业于东南大学信息科学与工程学院，获工学博士学位。主要研究方向为电磁场与微波技术及计算电磁学。教授过的课程有《工程电磁学与计算电磁学》和《电磁场边值问题数值分析》（都是研究生课程）。本人参与科研项目有国家自然科学基金项目 “区域分解积分方程法研究及其在微波毫米波LTCC无源集成电路中的应用”，与德国电磁仿真软件CST的合作,以及与美国波音公司合作项目“Onboard and off Board Communication”，还有863计划 “紧凑结构MIMO多天线技术及其信道的研究”等等。在国际国内核心刊物发表论文十数篇。

五、任课教师信息（包括主讲教师）：

Application Form For Opening Graduate Courses

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 chool (Department/Institute)：

Course Type: New Open □   Reopen □   Rename □（Please tick in □, the same below）

1. Course Introduction (including teaching goals and requirements) within 300 words:

The goal of the course is to make students learn and master how to use modern numerical analysis methods to solve problems in electromagnetic fields and waves, and have a platform to do researches on electromagnetic fields and waves.

The students is required to learn and master the fundamental theories of numerical methods and their applications in classes, and to learn more detailed and advanced materials and recent developments by reading journal articles and textbooks after classes.

2. Teaching Syllabus (including the content of chapters and sections. A sheet can be attached):

Chapter 1Fundamental Theory of Electromagnetic Field

Maxwell’s equations, Constitutive relations，Boundary conditions, Potential functions, Propagation characteristics, Scattering problems, Radiation problems.

Chapter 2Method of Lines (MoL)

Fundamental principle, Propagation characteristics of transmission lines, Discontinuity of transmission line, EM Scattering.

Chapter 3  Transmission Line Matrix (TLM) Method

Fundamental principle, Two-dimensional guided wave and EM scattering problems, Three-dimensional waveguide discontinuity and EM scattering problems.

Chapter 4 Mode Matching Method (MMM)

Fundamental principle, Guided wave problems, EM scattering by frequency selected surface.

Chapter 5  Finite Difference Method (FDM)

Construction of difference equations, Static field problem, Eigen-value problem of Helmholtz equation, Two- dimensional EM scattering.

Chapter 6 Iterative Method for Solving  

Description of Iterative Methods，Jacobi Method , Gauss-Seidel Method, Successive Over-Relaxation(SOR) & Symmetrical Successive Over-Relaxation(SSOR)

Chapter 7 Finite-Difference Time-Domain Method (FDTD) Method

Construction of difference equations in time domain, Boundary conditions, Exciting source, Solution of finite difference equations, Discontinuity of transmission line, Two-dimensional EM scattering, Three-dimensional EM scattering.

Chapter 8  Finite Difference Frequency Domain (FDFD) Method

Construction of difference equations in frequency domain, Boundary conditions, Solution of finite difference equations in frequency domain, Discontinuity of transmission line, Three-dimensional EM scattering, Radiation problem.

Chapter 9 Finite Element Method (FEM)

Fundamental principle, FEM for Laplace’s equation, FEM for Helmholtz’s equation, FEM for Maxwell’s equation.

Chapter 10  Solution of Symmetric Positive-Definite Matrices Conjugate Gradient Method-- Conjugate Gradient Method

Description of Problems，Conjugate Gradient Method(CG)，Precondition Conjugate Gradients(PCG)，Conjugate Gradients for Symmetric Complex or Indefinite Matrices

Chapter 11Method of Moments (MoM) and Variational Principle

Description of Variational Problems, Variational Formulation for Electromagnetic Field Problems, Fundamental principle, Basis functions, Testing functions, Wire antennas, Dipole and dipole array, Two-dimensional EM scattering, Three-dimensional EM scattering.

Chapter 12 Domain Decomposition Method (DDM)

Fundamental principle, DDM for Laplace’s equation, DDM for Helmholtz’s equation, DDM for Maxwell’s equation.

Chapter 13Vector Finite Elements

Description of Problems，Basis Functions for Triangle Finite Elements，Computation of Element Matrices，Continuity of Field with Matrix Coefficients

Chapter 14Boundary Element Method (BEM)

Fundamental principle, Static field problem, Waveguide discontinuity, Two-dimensional EM scattering, Three-dimensional EM scattering.

Chapter 15Spectral Domain Approach (SDA)

Fundamental principle, Static field problems, Full-wave analysis of integrated transmission lines, EM scattering by frequency selected surface, Microstrip antennas and array.

Chapter 16 Measured Equation of Invariance (MEI) Method

Concepts of MEI, Acceleration methods for MEI, MEI in time domain, Parameter extraction of VLSI interconnects, Two-dimensional EM scattering.

Chapter 17Field integral equations

Maxwell’s Equations in Integral Form，Boundary Conditions，Formulations of EFIE, MFIE and CFIE，Numerical Examples

Chapter 18Integral Equation-based Overlapped Domain Decomposition Method (IE-ODDM)

Introduction，IE-ODDM，Range of Buffer Region，Computational Complexity，IE-ODDM for Dielectric Objects，Numerical Examples

Chapter 19MLFMA-based Overlapped Domain Decomposition Method (IE-ODDM-MLFMA)

MLFMA and Preconditioner，IE-ODDM-MLFMA，Complexity and Characteristics of IE-ODDM-MLFMA，RWG-based and Cube-based Schemes of IE-ODDM-MLFMA，Numerical Examples

Chapter 20Impedance Matrix Interpolation Method

Matrix Element as Function of Frequency，Some Matrix Interpolation Methods，Optimization of Frequency Samples，Numerical Examples

3. Teaching Schedule:

Note: 1.Above one, two, and three items are used as teaching Syllabus in Chinese and announced on the Chinese website of Graduate School. The four and five items are preserved in Graduate School.

2. Course terms: Spring, Autumn , and Spring-Autumn term.  

3. The teaching languages for courses: Chinese, English or Chinese-English.

4. Applicable range of discipline: public, first-class discipline, second-class discipline, and third-class discipline.

5. Practice includes: experiment, investigation, research report, etc.

6. Teaching methods: lecture, seminar, practice, etc.

7. Examination for degree courses must be in paper.

8. Teaching material websites are those which have already been announced.

9. Brief introduction of chief lecturer should include: personal information (date of birth, gender, degree achieved, professional title), research direction, teaching and research achievements. (within 100-500 words)

4. Brief Introduction of Chief lecturer:

Hong Wei  was born in Hebei Province, P.R. China, on October 24, 1962. He received the B.S. degree from the Zhenzhou Institute of Technology, Zhenzhou, China, in 1982, and the M.S. and Ph.D degrees from Southeast University, Nanjing, China, in 1985 and 1988, respectively, all in radio engineering.

Since 1988, he has been with the State Key Laboratory of Millimeter Waves, Southeast University, and is currently a professor and the Associate Dean of the Department of Radio Engineering. In 1993, 1995, 1996, 1997 and 1998, he was a short-term Visiting Scholar with the University of California at Berkeley and at Santa Cruz, respectively. He has been engaged in numerical methods for electromagnetic problems, millimeter wave theory and technology, antennas, electromagnetic scattering, inverse scattering and propagation, RF front-end for mobile communications and the parameters extraction of interconnects in VLSI circuits etc. He has authored and co-authored over 200 technical publications, and authored a book of Principle and Application of the Method of Lines. He was awarded twice the first-class Science and Technology Progress Prizes issued by the State Education Commission in 1992 and 1994 respectively, awarded the fourth-class National Natural Science Prize in 1991, and the third-class Science and Technology Progress Prize of Jiangsu Province. Besides, he is the recipient of the Trans-Century Training Programme Foundation for the Talents issued by the State Education Commission, the Foundation for China Distinguished Young Investigators issued by NSFC, the award of Distinguished China Doctorate Receiptients issued by the State Education Commission, and the JiangSu Young Scientist Award issued by JiangSu Province Government.

Professor Hong is a member of IEEE, Senior member of CIE, and served as the reviewer for many technique journals, such as IEEE Trans. on MTT, IEEE Trans. on AP, IEE Proc.-H, Electron. Lett. etc.

Sun Lianyou received M.Sc. degree in applied mathematics from Fudan University, Shanghai, China, in 1990. PhD degree in electromagnetic field and microwave technology from Southeast University, Nanjing, China, in 2003.

He worked at Southeast University, Nanjing, China, firstly in Department of Applied Mathematics as a lecturer from 1990 to 1997, and then in Department of Radio Engineering as a associate professor from 1998 to 2005. With Financial support of China Scholarship Council, he pursued his postdoctoral studies in computational electromagnetics at McGill University, Montreal, Canada from Aug. 2005 to Aug. 2006. His current interests are in numerical methods for electromagnetic problems, especially for large scale problems. He also is a co-authorof a book:Domain Decomposition Methods for Solving the Electromagnetic field Boundary Value Problems,Beijing, China: Science Press, 2005. He has published more than ten papers on computational electromagnetics.

Li Wei-Dong was born in Henan Province, China, in March 1975. He received the M.S. degree in computational mathematics and the Ph.D degree in electromagnetic fields and microwave technology from Southeast University, Nanjing, China, in 2003 and 2007, respectively. In April 2007, he joined the State Key Laboratory of Millimeter Waves, Southeast University. From January 2008 to January 2009, he was a Visiting Scholar with the Technische Universität Darmstadt, Germany. His current research interests include accurate numerical modeling, fast algorithm, parallel computing in computational EM, and frequency selective surfaces. He is also interested in numerical analysis and numerical methods for partial differential equations.

5. Lecturer Information (include chief lecturer)