MS004310-计算电磁学中的快速算法

研究生课程开设申请表

 开课院（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）

 介绍国际相关领域的研究进展与现状，将国际上相关领域的最新研究成果介绍给学生，并与现有的科研项目紧密地结合起来。同时讲授本领域内的基础知识。在计算电磁学领域培养一定的独立科研工作能力和创新能力。

二、教学大纲（含章节目录）：（可附页）

1. 计算电磁学的历史、现状与未来

• 选题的依据及重要意义

• 国际上相关领域的进展与现状

• 国际上相关领域的最新研究成果

• 计算电磁学是一门涉及数学、物理学及计算机科学的学科

• 我们为什么要考虑快速算法？

• 怎样与现有的科研项目最紧密地结合，以解决实际问题?

• 介绍目前尚未解决的、具有挑战性的问题

2. Green函数与积分方程

• 自由空间中的Green函数

• 半空间中的Green函数

• 多层媒质中的Green函数

• 电场并矢Green函数

• 磁场并矢Green函数

• 混合位场Green函数

• 电场积分方程--- 介电体情况

• 电场积分方程--- 理想导体情况

• 磁场积分方程--- 理想导体情况

• 混合积分方程--- 理想导体情况

• 体积分方程

• 表面积分方程

3. 积分方程的数值解法 ---- 矩量法

• 介电体问题的矩量法（体基函数）

• 理想导体问题的矩量法（表面RWG基函数）

• 细导线问题的矩量法（线基函数）

• 理想导体和细导线问题的矩量法（线-面接头基函数）

• 复杂问题的矩量法

4. 自由空间中平面理想导体结构的二维CG-FFT算法

• 平面理想导体结构的剖分及二维矩形网格

• 电场积分方程的简化

• 二维离散卷积及快速傅立叶变换

• 伴随算子

• 共扼梯度方法

• 应用：电磁散射问题；Benchmarks

5. 半空间及多层媒质中平面理想导体结构的二维CG-FFT算法

• 半空间及多层媒质中电场积分方程的简化

• 二维离散卷积、离散相关及快速傅立叶变换

• 伴随算子及共扼梯度方法

• 应用：埋地物体的探测；电路仿真

6. 自由空间中三维介电体的三维CG-FFT算法

• 三维介电体的剖分及三维立方体网格

• 电场积分方程的简化

• 三维离散卷积及快速傅立叶变换

• 伴随算子及共扼梯度方法

• 应用：生物体的电磁仿真；微波成像

7. 半空间及多层媒质中三维介电体的三维CG-FFT算法

• 半空间及多层媒质中电场积分方程的简化

• 三维离散卷积、离散相关及快速傅立叶变换

• 伴随算子及共扼梯度方法

• 应用：埋地物体的仿真；埋地物体的探测

8. 自由空间及半空间中三维介电体的快速近似方法

• 应用近似方法的意义

• Born近似

• 推广的Born近似

• 高阶推广的Born近似

9. 平面理想导体结构的二维预相关FFT算法及自适应积分方程法

• 平面理想导体结构的剖分及RWG三角形网格

• 由RWG三角形网格向规则的矩形网格的变换

• 自由空间中平面理想导体结构的二维预相关FFT算法及自适应积分方程法

• 半空间中平面理想导体结构的二维预相关FFT算法及自适应积分方程法

• 多层媒质中平面理想导体结构的二维预相关FFT算法及自适应积分方程法

• 应用：电磁散射；埋地物体的仿真；电路仿真

10.三维介电体及导体的三维预相关FFT算法及自适应积分方程法

• 剖分：三维导体--- RWG三角形网格；三维介电体：四面体网格

• 由RWG三角形网格向规则的立方体网格的变换

• 由四面体网格向规则的立方体网格的变换

• 自由空间中三维介电体及导体的三维预相关FFT算法及自适应积分方程法

• 半空间中三维介电体及导体的三维预相关FFT算法及自适应积分方程法

• 多层媒质中三维介电体及导体的三维预相关FFT算法及自适应积分方程法

• 应用：电磁散射；埋地物体的仿真；电路仿真

11.快速多极子方法的基本概念简介

• 概念简介

• 静电问题中的快速多极子方法

12. 二维电磁问题的快速多极子方法

• 二维Green函数的加法定理

• Green函数的有效因子化

• 转移算子的对角化

• 对角化转移算子的另外一种推导方法

• 聚集、转移及扩散的物理意义

• 辐射方向图的带宽

• 误差控制

• 应用：电磁散射及天线问题

13. 二维电磁问题中的多层快速多极子算法

• 多层方法的意义

• 二维树状结构的建立

• Green函数的有效因子化

• 聚集过程

• 转移过程

• 扩散过程

• 疏-密插值及密-疏插值

• 多层快速多极子算法的内存需求量及计算复杂度

14. 关于快速多极子方法和多层快速多极子算法的进一步补充说明

• 全域插值（精确）

• 局域插值（可做到指数级地准确）

• 组

• 组的表示

• Green函数的平面波表示

15. 三维电磁问题的快速多极子方法

• 三维Green函数的加法定理

• 聚集过程

• 转移过程

• 扩散过程

• 误差分析：Green函数中的截断误差；数值积分误差

• 内存需求量及计算复杂度

16. 三维电磁问题中的多层快速多极子算法

• 三维Green函数的有效因子化

• 三维树状结构的建立

• 聚集过程、转移过程及扩散过程

• 疏-密插值及密-疏插值

• 误差分析：局域插值中的误差

• 内存需求量及计算复杂度

• 应用分块对角矩阵改善条件数

17. 三维电磁问题中的多层快速多极子与快速远场近似混合算法

• 多层快速多极子与快速远场近似混合算法的意义：处理超大规模电磁结构

• 快速远场近似

• 快速远场近似的条件

• 树状结构的最底层与最高层

• 多层快速多极子与快速远场近似混合算法的物理描述

• 内存需求量及计算复杂度

18. 三维电磁问题中的多从层快速多极子、射线传输快速多极子与快速远场近似混合算法

• 多层快速多极子、射线传输快速多极子与快速远场近似混合算法的意义：处理超大规模电磁结构，并能控制误差

• 加窗的转移算子

• 转移算子的方向图

• 射线传输快速多极子算法

• 多层快速多极子、射线传输快速多极子与快速远场近似混合算法

• 射线传输快速多极子算法与快速远场近似的关系

三、教学周历

(第1周由崔铁军教授讲授，其它由张剑锋讲师讲授)

四、主讲教师简介：

崔铁军，男，生于1965年9月。1987年毕业于西安电子科技大学，获工程学士学位。1989年和1993年分别在西安电子科技大学获硕士及博士学位，后留校从事教学与科研工作。1993年11月破格提升为副教授。1995年至1997年，获得德国Alexander von Humboldt Foundation（洪堡基金会）的资助，在德国Karlsruhe大学作为洪堡学者进行合作研究。1997年至1999年，在美国University of Illinois at Urbana-Champaign作博士后Research Associate；2000年至2002年，被University of Illinois at Urbana-Champaign聘为Research Scientist。2001年10月被聘为东南大学无线电工程系教授、博士生导师、教育部“长江学者奖励计划”特聘教授。现为东南大学信息科学与工程学院副院长、毫米波国家重点实验室副主任、东南大学目标特性与识别研究所所长，国际著名刊物IEEE Transactions on Geoscience and Remote Sensing的副主编。

 主要学术任职包括：国际著名刊物IEEE Transactions on Geoscience and Remote Sensing 的副主编；IEEE Antennas and Propagation Magazine编委会成员；IEEE高级会员；国际无线电联盟会员；中国电子学会天线学会电磁散射与逆散射专业委员会副主任委员；中国物理学会计算电磁学专业委员会副主任委员；中国兵工学会电磁专业委员会委员；南京市留学归国人员联谊会常务理事；江苏省侨界青年总会第一届理事会理事。曾任2004年大型国际会议“电磁研究进展（Progress in Electromagnetic Research Symposium，PIERS）”的技术委员会副主席、2005年“亚太微波会议（Asian Pacific Microwave Conference, APMC）”技术委员会联合主席、2008年“微波毫米波技术国际会议（International Conference on Microwave and Millimeter Wave Technology）”技术委员会联合主席、2008年“新型人工电磁材料国际研讨会（International Workshop on Metamaterials）”大会主席等。

张剑锋，男，生于1979年5月。2000年毕业于山东工业大学，获工程学士学位。2004年毕业于南京电子技术研究所，获硕士学位。2008年于东南大学获博士学位，后留校从事教学和科研工作。

 曾获中国兵工学会优秀论文一等奖，在IEEE Transactions on Antennas and Propagation 和 Physical Review B 上各发表论文一篇，并在国际会议上发表论文多篇。主要研究方向为计算电磁学、快速算法、多层媒质理论等。

五、任课教师信息（包括主讲教师）：

Application Form For Opening Graduate Courses

School (Department/Institute)：School of Information Science and Engineering

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

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

The research development, current situation and the state-of-the-art of computational electromagnetics will be introduced. Moreover, the fundament of this interdisciplinary will be thoroughly taught. Students are expected to acquire the abilities of independent researching and innovation.

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

1. An Introduction: The History, Current Status, and Future

• International research progresses and current status

• International latest research achievement

• Motivation of fast algorithm

• How to settle practice problems

• The unresolved and more challengeable problems

2. Green's Functions and Integral Equations

• Green's function in free space

• Green's function in half-space

• Green's function in multi-layered media

• Electric field dyadic Green's function

• Magnetic field dyadic Green's function

• Combined field dyadic Green's function

• Electric field integral equation for dielectric objects

• Electric field integral equation for perfectly conductor

• Magnetic field integral equation for perfectly conductor

• Combined field integral equation for perfectly conductor

• Volume integral equation

• Surface integral equation

3. The Method of Moments

• MoM for dielectric bodies

• MoM for PEC bodies

• MoM for wire structures

• Wire-surface Junction Basis

• MoM for more complex problems

4. CG-FFT for 2D PEC Objects in Free Space

• Meshing strategy

• Simplification of EFIE

• Discrete convolution and FFT in 2D case

• Adjoint operator

• Conjugate gradient method

• Applications

5. CG-FFT for 2D PEC Objects in Half-Space and Multi-Layered Media

• Simplification of EFIE for Half-Space and Multi-Layered Media

• Discrete convolution, discrete correlation and FFT in 2D Case

• Adjoint operator and CG method

• Applications

6. CG-FFT for 3D Dielectric Objects in Free Space

• Meshing strategy

• Simplification of EFIE for free space

• Discrete convolution and FFT in 3D Case

• Adjoint operator and CG method

• Applications

7. CG-FFT for 3D Dielectric Objects in Half-Space and Multi-Layered Media

• Simplification of EFIE for Half-Space and Multi-Layered Media

• Discrete convolution, discrete correlation and FFT in 3D Case

• Adjoint operator and CG method

• Applications

8. Fast Approximation method in Free Space and Half-Space

• Born approximation

• Extended Born approximation

• Extended high-order Born approximation

9. Adaptive Integral Method and Precorrected FFT Algorithm for 2D Objects

• Meshing strategy

• Transforming triangular mesh to rectangular mesh

• Adaptive integral method and precorrected FFT algorithm for 2D objects in free sapce

• Adaptive integral method and precorrected FFT algorithm for 2D objects in half-sapce

• Adaptive integral method and precorrected FFT algorithm for 2D objects in multi-layered media

• Applications

10.Adaptive Integral Method and Precorrected FFT Algorithm for 3D Objects

• Meshing strategy

• Transforming tetrahedral mesh to hexahedron mesh

• Adaptive integral method and precorrected FFT algorithm for 3D objects in free sapce

• Adaptive integral method and precorrected FFT algorithm for 3D objects in half-sapce

• Adaptive integral method and precorrected FFT algorithm for 3D objects in multi-layered media

• Applications

11.Principle of the Fast Multipole Method

• Introduction

• Fast multipole method in static case

12. Fast Multipole Method for 2D Problems

• Addition theorem for 2D Green's functions

• Effective factorize of 2D Green's functions

• Diagonalization of the translator

• An alternative derivation of the Green's function's factorization

• Physical interpretation of aggregation, translation and disaggregation

• Bandwidth of the radiation pattern

• Error control

• Applications

13. Multilevel Fast Multipole Algorithm for 2D Problems

• Motivation for multilevel algorithm

• Making a quad tree structure

• Effective factorize of 2D Green's functions

• Aggregation

• Translation

• Disaggregation

• Interpolation

• Complexity analysis

14. More on FMM and MLFMA

• Global interpolation

• Local interpolation

• Grouping

15. Fast Multipole Method for 3D Problems

• Addition theorem for 3D Green's functions

• Aggregation

• Translation

• Disaggregation

• Error analysis and control

• Complexity analysis

16. Multilevel Fast Multipole Algorithm for 3D Problems

• Effective factorize of 3D Green's functions

• Making a octree structure

• Aggregation, translation and disaggregation

• Interpolation

• Error analysis and control

• Complexity analysis

17. Acceleration of MLFMA Using Fast Far-Field Approxiamation

• Introduction

• Fast far-field approximation

• Criteria to use FAFFA

• Combination of MLFMA and FAFFA

• Complexity analysis

18. Combination of MLMFA, RPFMA, and FAFFA Algorithm

• Introduction

• Applied windows function to translation operator

• Pattern of translation operator

• Principle of RPFMA

• Combination of MLMFA, RPFMA, and FAFFA Algorithm

• Connection of RPFMA and FAFFA

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:

Tie Jun Cui was born in September 1965, in Hebei, China. He received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from Xidian University, Xi'an, China, in 1987, 1990, and 1993, respectively.

In March 1993, he joined the Department of Electromagnetic Engineering, Xidian University, and was promoted to an Associate Professor in November 1993. From 1995 to 1997 he was a Research Fellow with the Institut fur Hochstfrequenztechnik und Elektronik (IHE) at the University of Karlsruhe, Germany. In July 1997, he joined the Center for Computational Electromagnetics, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, first as a Postdoctoral Research Associate and then a Research Scientist. In September 2001, he became a Cheung-Kong Professor with the Department of Radio Engineering, Southeast University, Nanjing, P. R. China. Currently, he is the Associate Director of the State Key Laboratory of Millimeter Waves, and the Center for Computational Electromagnetics.

Dr. Cui is the author of four book chapters. He has published over 170 scientific articles in international journals, including 48 IEEE Transactions papers and over 80 physics/optics papers in Science, Physical Review Letters, Physical Review B, Physical Review E, Applied Physics Letters, Optics Letters, and Optics Express, etc. His research interests include metamaterials, wave propagations, scattering, inverse scattering, metamaterials, landmine detection, geophysical subsurface sensing, fast algorithms, microwave and millimeter wave circuits and antennas simulations. Currently, he is a principal investigator of several national projects.

Dr. Cui was awarded a Third Prize of Science and Technology Progress by the Ministry of Electronics, China, in 1991, and a Research Fellowship from the Alexander von Humboldt Foundation, Bonn, Germany, in 1995, received a Young Scientist Award from the International Union of Radio Science (URSI) in 1999, was awarded a Cheung Kong Professor under the Cheung Kong Scholar Program by the Ministry of Education, China, in 2001, and received the National Science Foundation of China for Distinguished Young Scholars in 2002. He received several Best Paper Awards from the National and International Conferences and Organizations, including a Best Paper Award in Natural Science (the first place) by Nanjing Government, China, in 2005.

Dr. Cui is a senior member of IEEE and a member of URSI (Commission B). He serves as an Editorial Staff in IEEE Antennas and Propagation Magazine, and is now an Associate Editor in IEEE Transactions on Geoscience and Remote Sensing.

Jian Feng Zhang was born in May 1979, in Shandong, China. He received the B.E. degree from Shandong University of Technology (now the Shandong University), Shandong, China, in 2000, the M. E. degree from the 14th Research Institute of CETC, China, 2004, and the Ph. D degree from Southeast University, Nanjing, China, 2008. His research interests include computational electromagnetics, fast algorithms, multilayered media, etc.

5. Lecturer Information (include chief lecturer)